@article{12916,
  abstract     = {We apply a variant of the square-sieve to produce an upper bound for the number of rational points of bounded height on a family of surfaces that admit a fibration over P1 whose general fibre is a hyperelliptic curve. The implied constant does not depend on the coefficients of the polynomial defining the surface.
},
  author       = {Bonolis, Dante and Browning, Timothy D},
  issn         = {2036-2145},
  journal      = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
  number       = {1},
  pages        = {173--204},
  publisher    = {Scuola Normale Superiore - Edizioni della Normale},
  title        = {{Uniform bounds for rational points on hyperelliptic fibrations}},
  doi          = {10.2422/2036-2145.202010_018},
  volume       = {24},
  year         = {2023},
}

@article{9364,
  abstract     = {Let t : Fp → C be a complex valued function on Fp. A classical problem in analytic number theory is bounding the maximum M(t) := max 0≤H<p ∣ 1/√p ∑ 0≤n<H t (n) ∣ of the absolute value of the incomplete sums(1/√p)∑0≤n<H t (n). In this very general context one of the most important results is the Pólya–Vinogradov bound M(t)≤IIˆtII∞ log 3p, where ˆt : Fp → C is the normalized Fourier transform of t. In this paper we provide a lower bound for certain incomplete Kloosterman sums, namely we prove that for any ε > 0 there exists a large subset of a ∈ F×p such that for kl a,1,p : x → e((ax+x) / p) we have M(kla,1,p) ≥ (1−ε/√2π + o(1)) log log p, as p→∞. Finally, we prove a result on the growth of the moments of {M (kla,1,p)}a∈F×p. 2020 Mathematics Subject Classification: 11L03, 11T23 (Primary); 14F20, 60F10 (Secondary).},
  author       = {Bonolis, Dante},
  issn         = {1469-8064},
  journal      = {Mathematical Proceedings of the Cambridge Philosophical Society},
  number       = {3},
  pages        = {563 -- 590},
  publisher    = {Cambridge University Press},
  title        = {{On the size of the maximum of incomplete Kloosterman sums}},
  doi          = {10.1017/S030500412100030X},
  volume       = {172},
  year         = {2022},
}

@article{10711,
  abstract     = {In this paper, we investigate the distribution of the maximum of partial sums of families of  m -periodic complex-valued functions satisfying certain conditions. We obtain precise uniform estimates for the distribution function of this maximum in a near-optimal range. Our results apply to partial sums of Kloosterman sums and other families of  ℓ -adic trace functions, and are as strong as those obtained by Bober, Goldmakher, Granville and Koukoulopoulos for character sums. In particular, we improve on the recent work of the third author for Birch sums. However, unlike character sums, we are able to construct families of  m -periodic complex-valued functions which satisfy our conditions, but for which the Pólya–Vinogradov inequality is sharp.},
  author       = {Autissier, Pascal and Bonolis, Dante and Lamzouri, Youness},
  issn         = {1570-5846},
  journal      = {Compositio Mathematica},
  keywords     = {Algebra and Number Theory},
  number       = {7},
  pages        = {1610--1651},
  publisher    = {Cambridge University Press},
  title        = {{The distribution of the maximum of partial sums of Kloosterman sums and other trace functions}},
  doi          = {10.1112/s0010437x21007351},
  volume       = {157},
  year         = {2021},
}