[{"page":"1115-1203","publication":"Annals of Mathematics","issue":"3","type":"journal_article","day":"01","status":"public","intvolume":"       197","department":[{"_id":"TiBr"}],"date_created":"2020-10-19T14:28:50Z","oaworkID":1,"date_published":"2023-05-01T00:00:00Z","article_type":"original","month":"05","language":[{"iso":"eng"}],"publisher":"Princeton University","article_processing_charge":"No","date_updated":"2025-08-11T11:59:49Z","volume":197,"oa":1,"arxiv":1,"oa_version":"Preprint","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0003-486X"]},"_id":"8682","citation":{"ieee":"T. D. Browning, P. L. Boudec, and W. Sawin, “The Hasse principle for random Fano hypersurfaces,” <i>Annals of Mathematics</i>, vol. 197, no. 3. Princeton University, pp. 1115–1203, 2023.","apa":"Browning, T. D., Boudec, P. L., &#38; Sawin, W. (2023). The Hasse principle for random Fano hypersurfaces. <i>Annals of Mathematics</i>. Princeton University. <a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">https://doi.org/10.4007/annals.2023.197.3.3</a>","chicago":"Browning, Timothy D, Pierre Le Boudec, and Will Sawin. “The Hasse Principle for Random Fano Hypersurfaces.” <i>Annals of Mathematics</i>. Princeton University, 2023. <a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">https://doi.org/10.4007/annals.2023.197.3.3</a>.","mla":"Browning, Timothy D., et al. “The Hasse Principle for Random Fano Hypersurfaces.” <i>Annals of Mathematics</i>, vol. 197, no. 3, Princeton University, 2023, pp. 1115–203, doi:<a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">10.4007/annals.2023.197.3.3</a>.","ama":"Browning TD, Boudec PL, Sawin W. The Hasse principle for random Fano hypersurfaces. <i>Annals of Mathematics</i>. 2023;197(3):1115-1203. doi:<a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">10.4007/annals.2023.197.3.3</a>","short":"T.D. Browning, P.L. Boudec, W. Sawin, Annals of Mathematics 197 (2023) 1115–1203.","ista":"Browning TD, Boudec PL, Sawin W. 2023. The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. 197(3), 1115–1203."},"publication_status":"published","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","first_name":"Timothy D"},{"first_name":"Pierre Le","full_name":"Boudec, Pierre Le","last_name":"Boudec"},{"first_name":"Will","last_name":"Sawin","full_name":"Sawin, Will"}],"abstract":[{"lang":"eng","text":"It is known that the Brauer--Manin obstruction to the Hasse principle is vacuous for smooth Fano hypersurfaces of dimension at least 3 over any number field. Moreover, for such varieties it follows from a general conjecture of Colliot-Thélène that the Brauer--Manin obstruction to the Hasse principle should be the only one, so that the Hasse principle is expected to hold. Working over the field of rational numbers and ordering Fano hypersurfaces of fixed degree and dimension by height, we prove that almost every such hypersurface satisfies the Hasse principle provided that the dimension is at least 3. This proves a conjecture of Poonen and Voloch in every case except for cubic surfaces."}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2006.02356"}],"isi":1,"related_material":{"link":[{"relation":"press_release","description":"News on IST Homepage","url":"https://ist.ac.at/en/news/when-is-necessary-sufficient/"}]},"year":"2023","doi":"10.4007/annals.2023.197.3.3","title":"The Hasse principle for random Fano hypersurfaces","external_id":{"isi":["000966611000003"],"oaworkID":["w3033938593"],"arxiv":["2006.02356"]}},{"language":[{"iso":"eng"}],"publisher":"Annals of Mathematics, Princeton U","date_published":"2018-07-01T00:00:00Z","article_type":"original","month":"07","date_created":"2020-09-17T10:42:22Z","status":"public","intvolume":"       188","type":"journal_article","day":"01","page":"315-380","publication":"Annals of Mathematics","issue":"1","title":"On the local Birkhoff conjecture for convex billiards","external_id":{"arxiv":["1612.09194"]},"year":"2018","doi":"10.4007/annals.2018.188.1.6","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.09194"}],"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"author":[{"orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","last_name":"Kaloshin","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"first_name":"Alfonso","full_name":"Sorrentino, Alfonso","last_name":"Sorrentino"}],"abstract":[{"lang":"eng","text":"The classical Birkhoff conjecture claims that the boundary of a strictly convex integrable billiard table is necessarily an ellipse (or a circle as a special case). In this article we prove a complete local version of this conjecture: a small integrable perturbation of an ellipse must be an ellipse. This extends and completes the result in Avila-De Simoi-Kaloshin, where nearly circular domains were considered. One of the crucial ideas in the proof is to extend action-angle coordinates for elliptic billiards into complex domains (with respect to the angle), and to thoroughly analyze the nature of their complex singularities. As an application, we are able to prove some spectral rigidity results for elliptic domains."}],"citation":{"ama":"Kaloshin V, Sorrentino A. On the local Birkhoff conjecture for convex billiards. <i>Annals of Mathematics</i>. 2018;188(1):315-380. doi:<a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">10.4007/annals.2018.188.1.6</a>","mla":"Kaloshin, Vadim, and Alfonso Sorrentino. “On the Local Birkhoff Conjecture for Convex Billiards.” <i>Annals of Mathematics</i>, vol. 188, no. 1, Annals of Mathematics, Princeton U, 2018, pp. 315–80, doi:<a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">10.4007/annals.2018.188.1.6</a>.","ista":"Kaloshin V, Sorrentino A. 2018. On the local Birkhoff conjecture for convex billiards. Annals of Mathematics. 188(1), 315–380.","short":"V. Kaloshin, A. Sorrentino, Annals of Mathematics 188 (2018) 315–380.","apa":"Kaloshin, V., &#38; Sorrentino, A. (2018). On the local Birkhoff conjecture for convex billiards. <i>Annals of Mathematics</i>. Annals of Mathematics, Princeton U. <a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">https://doi.org/10.4007/annals.2018.188.1.6</a>","ieee":"V. Kaloshin and A. Sorrentino, “On the local Birkhoff conjecture for convex billiards,” <i>Annals of Mathematics</i>, vol. 188, no. 1. Annals of Mathematics, Princeton U, pp. 315–380, 2018.","chicago":"Kaloshin, Vadim, and Alfonso Sorrentino. “On the Local Birkhoff Conjecture for Convex Billiards.” <i>Annals of Mathematics</i>. Annals of Mathematics, Princeton U, 2018. <a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">https://doi.org/10.4007/annals.2018.188.1.6</a>."},"publication_status":"published","quality_controlled":"1","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","publication_identifier":{"issn":["0003-486X"]},"_id":"8421","article_processing_charge":"No","volume":188,"oa":1,"date_updated":"2021-01-12T08:19:10Z","arxiv":1},{"page":"277-314","issue":"1","publication":"Annals of Mathematics","status":"public","intvolume":"       186","type":"journal_article","day":"01","date_created":"2020-09-17T10:46:42Z","language":[{"iso":"eng"}],"publisher":"Annals of Mathematics","article_type":"original","date_published":"2017-07-01T00:00:00Z","month":"07","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","oa_version":"Preprint","_id":"8427","extern":"1","publication_identifier":{"issn":["0003-486X"]},"oa":1,"volume":186,"date_updated":"2021-01-12T08:19:12Z","article_processing_charge":"No","arxiv":1,"author":[{"last_name":"De Simoi","full_name":"De Simoi, Jacopo","first_name":"Jacopo"},{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim","last_name":"Kaloshin","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628"},{"full_name":"Wei, Qiaoling","last_name":"Wei","first_name":"Qiaoling"}],"abstract":[{"text":"We show that any sufficiently (finitely) smooth ℤ₂-symmetric strictly convex domain sufficiently close to a circle is dynamically spectrally rigid; i.e., all deformations among domains in the same class that preserve the length of all periodic orbits of the associated billiard flow must necessarily be isometric deformations. This gives a partial answer to a question of P. Sarnak.","lang":"eng"}],"publication_status":"published","citation":{"ista":"De Simoi J, Kaloshin V, Wei Q. 2017. Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle. Annals of Mathematics. 186(1), 277–314.","short":"J. De Simoi, V. Kaloshin, Q. Wei, Annals of Mathematics 186 (2017) 277–314.","ama":"De Simoi J, Kaloshin V, Wei Q. Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle. <i>Annals of Mathematics</i>. 2017;186(1):277-314. doi:<a href=\"https://doi.org/10.4007/annals.2017.186.1.7\">10.4007/annals.2017.186.1.7</a>","mla":"De Simoi, Jacopo, et al. “Dynamical Spectral Rigidity among Z2-Symmetric Strictly Convex Domains Close to a Circle.” <i>Annals of Mathematics</i>, vol. 186, no. 1, Annals of Mathematics, 2017, pp. 277–314, doi:<a href=\"https://doi.org/10.4007/annals.2017.186.1.7\">10.4007/annals.2017.186.1.7</a>.","chicago":"De Simoi, Jacopo, Vadim Kaloshin, and Qiaoling Wei. “Dynamical Spectral Rigidity among Z2-Symmetric Strictly Convex Domains Close to a Circle.” <i>Annals of Mathematics</i>. Annals of Mathematics, 2017. <a href=\"https://doi.org/10.4007/annals.2017.186.1.7\">https://doi.org/10.4007/annals.2017.186.1.7</a>.","ieee":"J. De Simoi, V. Kaloshin, and Q. Wei, “Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle,” <i>Annals of Mathematics</i>, vol. 186, no. 1. Annals of Mathematics, pp. 277–314, 2017.","apa":"De Simoi, J., Kaloshin, V., &#38; Wei, Q. (2017). Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle. <i>Annals of Mathematics</i>. Annals of Mathematics. <a href=\"https://doi.org/10.4007/annals.2017.186.1.7\">https://doi.org/10.4007/annals.2017.186.1.7</a>"},"main_file_link":[{"url":"https://arxiv.org/abs/1606.00230","open_access":"1"}],"external_id":{"arxiv":["1606.00230"]},"title":"Dynamical spectral rigidity among Z2-symmetric strictly convex domains close to a circle","year":"2017","doi":"10.4007/annals.2017.186.1.7"},{"date_created":"2020-09-18T10:46:22Z","language":[{"iso":"eng"}],"publisher":"Princeton University Press","title":"An integrable deformation of an ellipse of small eccentricity is an ellipse","date_published":"2016-09-01T00:00:00Z","article_type":"original","doi":"10.4007/annals.2016.184.2.5","year":"2016","month":"09","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","quality_controlled":"1","_id":"8496","publication_identifier":{"issn":["0003-486X"]},"extern":"1","volume":184,"date_updated":"2021-01-12T08:19:40Z","article_processing_charge":"No","page":"527-558","issue":"2","publication":"Annals of Mathematics","author":[{"full_name":"Avila, Artur","last_name":"Avila","first_name":"Artur"},{"full_name":"De Simoi, Jacopo","last_name":"De Simoi","first_name":"Jacopo"},{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","first_name":"Vadim"}],"status":"public","intvolume":"       184","type":"journal_article","publication_status":"published","citation":{"mla":"Avila, Artur, et al. “An Integrable Deformation of an Ellipse of Small Eccentricity Is an Ellipse.” <i>Annals of Mathematics</i>, vol. 184, no. 2, Princeton University Press, 2016, pp. 527–58, doi:<a href=\"https://doi.org/10.4007/annals.2016.184.2.5\">10.4007/annals.2016.184.2.5</a>.","ama":"Avila A, De Simoi J, Kaloshin V. An integrable deformation of an ellipse of small eccentricity is an ellipse. <i>Annals of Mathematics</i>. 2016;184(2):527-558. doi:<a href=\"https://doi.org/10.4007/annals.2016.184.2.5\">10.4007/annals.2016.184.2.5</a>","ista":"Avila A, De Simoi J, Kaloshin V. 2016. An integrable deformation of an ellipse of small eccentricity is an ellipse. Annals of Mathematics. 184(2), 527–558.","short":"A. Avila, J. De Simoi, V. Kaloshin, Annals of Mathematics 184 (2016) 527–558.","ieee":"A. Avila, J. De Simoi, and V. Kaloshin, “An integrable deformation of an ellipse of small eccentricity is an ellipse,” <i>Annals of Mathematics</i>, vol. 184, no. 2. Princeton University Press, pp. 527–558, 2016.","apa":"Avila, A., De Simoi, J., &#38; Kaloshin, V. (2016). An integrable deformation of an ellipse of small eccentricity is an ellipse. <i>Annals of Mathematics</i>. Princeton University Press. <a href=\"https://doi.org/10.4007/annals.2016.184.2.5\">https://doi.org/10.4007/annals.2016.184.2.5</a>","chicago":"Avila, Artur, Jacopo De Simoi, and Vadim Kaloshin. “An Integrable Deformation of an Ellipse of Small Eccentricity Is an Ellipse.” <i>Annals of Mathematics</i>. Princeton University Press, 2016. <a href=\"https://doi.org/10.4007/annals.2016.184.2.5\">https://doi.org/10.4007/annals.2016.184.2.5</a>."},"day":"01"},{"date_created":"2020-09-18T10:47:24Z","title":"Finiteness of central configurations of five bodies in the plane","publisher":"Princeton University Press","language":[{"iso":"eng"}],"year":"2012","month":"07","doi":"10.4007/annals.2012.176.1.10","date_published":"2012-07-01T00:00:00Z","article_type":"original","publication_identifier":{"issn":["0003-486X"]},"extern":"1","_id":"8503","quality_controlled":"1","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Annals of Mathematics","issue":"1","page":"535-588","article_processing_charge":"No","date_updated":"2021-01-12T08:19:44Z","volume":176,"abstract":[{"text":"We prove there are finitely many isometry classes of planar central configurations (also called relative equilibria) in the Newtonian 5-body problem, except perhaps if the 5-tuple of positive masses belongs to a given codimension 2 subvariety of the mass space.","lang":"eng"}],"intvolume":"       176","status":"public","author":[{"full_name":"Albouy, Alain","last_name":"Albouy","first_name":"Alain"},{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","last_name":"Kaloshin"}],"day":"01","citation":{"chicago":"Albouy, Alain, and Vadim Kaloshin. “Finiteness of Central Configurations of Five Bodies in the Plane.” <i>Annals of Mathematics</i>. Princeton University Press, 2012. <a href=\"https://doi.org/10.4007/annals.2012.176.1.10\">https://doi.org/10.4007/annals.2012.176.1.10</a>.","ieee":"A. Albouy and V. Kaloshin, “Finiteness of central configurations of five bodies in the plane,” <i>Annals of Mathematics</i>, vol. 176, no. 1. Princeton University Press, pp. 535–588, 2012.","apa":"Albouy, A., &#38; Kaloshin, V. (2012). Finiteness of central configurations of five bodies in the plane. <i>Annals of Mathematics</i>. Princeton University Press. <a href=\"https://doi.org/10.4007/annals.2012.176.1.10\">https://doi.org/10.4007/annals.2012.176.1.10</a>","short":"A. Albouy, V. Kaloshin, Annals of Mathematics 176 (2012) 535–588.","ista":"Albouy A, Kaloshin V. 2012. Finiteness of central configurations of five bodies in the plane. Annals of Mathematics. 176(1), 535–588.","mla":"Albouy, Alain, and Vadim Kaloshin. “Finiteness of Central Configurations of Five Bodies in the Plane.” <i>Annals of Mathematics</i>, vol. 176, no. 1, Princeton University Press, 2012, pp. 535–88, doi:<a href=\"https://doi.org/10.4007/annals.2012.176.1.10\">10.4007/annals.2012.176.1.10</a>.","ama":"Albouy A, Kaloshin V. Finiteness of central configurations of five bodies in the plane. <i>Annals of Mathematics</i>. 2012;176(1):535-588. doi:<a href=\"https://doi.org/10.4007/annals.2012.176.1.10\">10.4007/annals.2012.176.1.10</a>"},"publication_status":"published","type":"journal_article"},{"intvolume":"       165","abstract":[{"text":"For diffeomorphisms of smooth compact finite-dimensional manifolds, we consider the problem of how fast the number of periodic points with period n grows as a function of n. In many familiar cases (e.g., Anosov systems) the growth is exponential, but arbitrarily fast growth is possible; in fact, the first author has shown that arbitrarily fast growth is topologically (Baire) generic for C2 or smoother diffeomorphisms. In the present work we show that, by contrast, for a measure-theoretic notion of genericity we call “prevalence”, the growth is not much faster than exponential. Specifically, we show that for each ρ,δ>0, there is a prevalent set of C1+ρ (or smoother) diffeomorphisms for which the number of periodic n points is bounded above by exp(Cn1+δ) for some C independent of n. We also obtain a related bound on the decay of hyperbolicity of the periodic points as a function of n, and obtain the same results for 1-dimensional endomorphisms. The contrast between topologically generic and measure-theoretically generic behavior for the growth of the number of periodic points and the decay of their hyperbolicity show this to be a subtle and complex phenomenon, reminiscent of KAM theory. Here in Part I we state our results and describe the methods we use. We complete most of the proof in the 1-dimensional C2-smooth case and outline the remaining steps, deferred to Part II, that are needed to establish the general case.\r\n\r\nThe novel feature of the approach we develop in this paper is the introduction of Newton Interpolation Polynomials as a tool for perturbing trajectories of iterated maps.","lang":"eng"}],"status":"public","author":[{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","first_name":"Vadim"},{"first_name":"Brian","last_name":"Hunt","full_name":"Hunt, Brian"}],"day":"01","citation":{"ama":"Kaloshin V, Hunt B. Stretched exponential estimates on growth of the number of periodic points for prevalent diffeomorphisms I. <i>Annals of Mathematics</i>. 2007;165(1):89-170. doi:<a href=\"https://doi.org/10.4007/annals.2007.165.89\">10.4007/annals.2007.165.89</a>","mla":"Kaloshin, Vadim, and Brian Hunt. “Stretched Exponential Estimates on Growth of the Number of Periodic Points for Prevalent Diffeomorphisms I.” <i>Annals of Mathematics</i>, vol. 165, no. 1, Princeton University Press, 2007, pp. 89–170, doi:<a href=\"https://doi.org/10.4007/annals.2007.165.89\">10.4007/annals.2007.165.89</a>.","short":"V. Kaloshin, B. Hunt, Annals of Mathematics 165 (2007) 89–170.","ista":"Kaloshin V, Hunt B. 2007. Stretched exponential estimates on growth of the number of periodic points for prevalent diffeomorphisms I. Annals of Mathematics. 165(1), 89–170.","apa":"Kaloshin, V., &#38; Hunt, B. (2007). Stretched exponential estimates on growth of the number of periodic points for prevalent diffeomorphisms I. <i>Annals of Mathematics</i>. Princeton University Press. <a href=\"https://doi.org/10.4007/annals.2007.165.89\">https://doi.org/10.4007/annals.2007.165.89</a>","ieee":"V. Kaloshin and B. Hunt, “Stretched exponential estimates on growth of the number of periodic points for prevalent diffeomorphisms I,” <i>Annals of Mathematics</i>, vol. 165, no. 1. Princeton University Press, pp. 89–170, 2007.","chicago":"Kaloshin, Vadim, and Brian Hunt. “Stretched Exponential Estimates on Growth of the Number of Periodic Points for Prevalent Diffeomorphisms I.” <i>Annals of Mathematics</i>. Princeton University Press, 2007. <a href=\"https://doi.org/10.4007/annals.2007.165.89\">https://doi.org/10.4007/annals.2007.165.89</a>."},"publication_status":"published","type":"journal_article","publication_identifier":{"issn":["0003-486X"]},"extern":"1","_id":"8512","quality_controlled":"1","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Annals of Mathematics","issue":"1","page":"89-170","article_processing_charge":"No","volume":165,"date_updated":"2021-01-12T08:19:48Z","title":"Stretched exponential estimates on growth of the number of periodic points for prevalent diffeomorphisms I","publisher":"Princeton University Press","language":[{"iso":"eng"}],"year":"2007","month":"01","doi":"10.4007/annals.2007.165.89","date_published":"2007-01-01T00:00:00Z","article_type":"original","date_created":"2020-09-18T10:48:33Z"},{"date_created":"2020-09-18T10:50:28Z","language":[{"iso":"eng"}],"title":"An extension of the Artin-Mazur theorem","publisher":"JSTOR","date_published":"1999-09-01T00:00:00Z","article_type":"original","month":"09","year":"1999","doi":"10.2307/121093","oa_version":"None","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0003-486X"]},"extern":"1","_id":"8526","article_processing_charge":"No","page":"729-741","volume":150,"date_updated":"2021-01-12T08:19:53Z","publication":"The Annals of Mathematics","issue":"2","status":"public","author":[{"orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","last_name":"Kaloshin","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"}],"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"intvolume":"       150","type":"journal_article","day":"01","citation":{"chicago":"Kaloshin, Vadim. “An Extension of the Artin-Mazur Theorem.” <i>The Annals of Mathematics</i>. JSTOR, 1999. <a href=\"https://doi.org/10.2307/121093\">https://doi.org/10.2307/121093</a>.","ieee":"V. Kaloshin, “An extension of the Artin-Mazur theorem,” <i>The Annals of Mathematics</i>, vol. 150, no. 2. JSTOR, pp. 729–741, 1999.","apa":"Kaloshin, V. (1999). An extension of the Artin-Mazur theorem. <i>The Annals of Mathematics</i>. JSTOR. <a href=\"https://doi.org/10.2307/121093\">https://doi.org/10.2307/121093</a>","short":"V. Kaloshin, The Annals of Mathematics 150 (1999) 729–741.","ista":"Kaloshin V. 1999. An extension of the Artin-Mazur theorem. The Annals of Mathematics. 150(2), 729–741.","mla":"Kaloshin, Vadim. “An Extension of the Artin-Mazur Theorem.” <i>The Annals of Mathematics</i>, vol. 150, no. 2, JSTOR, 1999, pp. 729–41, doi:<a href=\"https://doi.org/10.2307/121093\">10.2307/121093</a>.","ama":"Kaloshin V. An extension of the Artin-Mazur theorem. <i>The Annals of Mathematics</i>. 1999;150(2):729-741. doi:<a href=\"https://doi.org/10.2307/121093\">10.2307/121093</a>"},"publication_status":"published"}]