---
OA_place: repository
OA_type: green
_id: '12312'
abstract:
- lang: eng
  text: "Let $\\ell$ be a prime number. We classify the subgroups $G$ of $\\operatorname{Sp}_4(\\mathbb{F}_\\ell)$
    and $\\operatorname{GSp}_4(\\mathbb{F}_\\ell)$ that act irreducibly on $\\mathbb{F}_\\ell^4$,
    but such that every element of $G$ fixes an $\\mathbb{F}_\\ell$-vector subspace
    of dimension 1. We use this classification to prove that the local-global principle
    for isogenies of degree $\\ell$ between abelian surfaces over number fields holds
    in many cases -- in particular, whenever the abelian surface has non-trivial endomorphisms
    and $\\ell$ is large enough with respect to the field of definition. Finally,
    we prove that there exist arbitrarily large primes $\\ell$ for which some abelian
    surface\r\n$A/\\mathbb{Q}$ fails the local-global principle for isogenies of degree
    $\\ell$."
acknowledgement: "It is a pleasure to thank Samuele Anni for his interest in this
  project and for several discussions on the topic of this paper, which led in particular
  to Remark 6.30 and to a better understanding of the difficulties with [6]. We also
  thank John Cullinan for correspondence about [6] and Barinder Banwait for his many
  insightful comments on the first version of this paper. Finally, we thank the referee
  for their thorough reading of the manuscript.\r\nOpen access funding provided by
  Università di Pisa within the CRUI-CARE Agreement. The authors have been partially
  supported by MIUR (Italy) through PRIN 2017 “Geometric, algebraic and analytic methods
  in arithmetic\" and PRIN 2022 “Semiabelian varieties, Galois representations and
  related Diophantine problems\", and by the University of Pisa through PRA 2018-19
  and 2022 “Spazi di moduli, rappresentazioni e strutture combinatorie\". The first
  author is a member of the INdAM group GNSAGA."
article_number: '18'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Davide
  full_name: Lombardo, Davide
  last_name: Lombardo
- first_name: Matteo
  full_name: Verzobio, Matteo
  id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
  last_name: Verzobio
  orcid: 0000-0002-0854-0306
date_created: 2023-01-16T11:45:53Z
date_published: 2024-01-26T00:00:00Z
date_updated: 2025-02-13T11:47:12Z
day: '26'
department:
- _id: TiBr
doi: 10.1007/s00029-023-00908-0
external_id:
  arxiv:
  - '2206.15240'
intvolume: '        30'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2206.15240
month: '01'
oa: 1
oa_version: Preprint
publication: Selecta Mathematica
publication_identifier:
  eissn:
  - 1420-9020
  issn:
  - 4321-1234
  issnl:
  - 1022-1824
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the local-global principle for isogenies of abelian surfaces
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2024'
...
---
_id: '12313'
abstract:
- lang: eng
  text: Let P be a nontorsion point on an elliptic curve defined over a number field
    K and consider the sequence {Bn}n∈N of the denominators of x(nP). We prove that
    every term of the sequence of the Bn has a primitive divisor for n greater than
    an effectively computable constant that we will explicitly compute. This constant
    will depend only on the model defining the curve.
acknowledgement: "This paper is part of the author’s PhD thesis at Università of Pisa.
  Moreover, this\r\nproject has received funding from the European Union’s Horizon
  2020 research\r\nand innovation programme under the Marie Skłodowska-Curie Grant
  Agreement\r\nNo. 101034413. I thank the referee for many helpful comments."
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Matteo
  full_name: Verzobio, Matteo
  id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
  last_name: Verzobio
  orcid: 0000-0002-0854-0306
citation:
  ama: Verzobio M. Some effectivity results for primitive divisors of elliptic divisibility 
    sequences. <i>Pacific Journal of Mathematics</i>. 2023;325(2):331-351. doi:<a
    href="https://doi.org/10.2140/pjm.2023.325.331">10.2140/pjm.2023.325.331</a>
  apa: Verzobio, M. (2023). Some effectivity results for primitive divisors of elliptic
    divisibility  sequences. <i>Pacific Journal of Mathematics</i>. Mathematical Sciences
    Publishers. <a href="https://doi.org/10.2140/pjm.2023.325.331">https://doi.org/10.2140/pjm.2023.325.331</a>
  chicago: Verzobio, Matteo. “Some Effectivity Results for Primitive Divisors of Elliptic
    Divisibility  Sequences.” <i>Pacific Journal of Mathematics</i>. Mathematical
    Sciences Publishers, 2023. <a href="https://doi.org/10.2140/pjm.2023.325.331">https://doi.org/10.2140/pjm.2023.325.331</a>.
  ieee: M. Verzobio, “Some effectivity results for primitive divisors of elliptic
    divisibility  sequences,” <i>Pacific Journal of Mathematics</i>, vol. 325, no.
    2. Mathematical Sciences Publishers, pp. 331–351, 2023.
  ista: Verzobio M. 2023. Some effectivity results for primitive divisors of elliptic
    divisibility  sequences. Pacific Journal of Mathematics. 325(2), 331–351.
  mla: Verzobio, Matteo. “Some Effectivity Results for Primitive Divisors of Elliptic
    Divisibility  Sequences.” <i>Pacific Journal of Mathematics</i>, vol. 325, no.
    2, Mathematical Sciences Publishers, 2023, pp. 331–51, doi:<a href="https://doi.org/10.2140/pjm.2023.325.331">10.2140/pjm.2023.325.331</a>.
  short: M. Verzobio, Pacific Journal of Mathematics 325 (2023) 331–351.
date_created: 2023-01-16T11:46:19Z
date_published: 2023-11-03T00:00:00Z
date_updated: 2023-12-13T11:18:14Z
day: '03'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.2140/pjm.2023.325.331
ec_funded: 1
external_id:
  arxiv:
  - '2001.02987'
  isi:
  - '001104766900001'
file:
- access_level: open_access
  checksum: b6218d16a72742d8bb38d6fc3c9bb8c6
  content_type: application/pdf
  creator: dernst
  date_created: 2023-11-13T09:50:41Z
  date_updated: 2023-11-13T09:50:41Z
  file_id: '14525'
  file_name: 2023_PacificJourMaths_Verzobio.pdf
  file_size: 389897
  relation: main_file
  success: 1
file_date_updated: 2023-11-13T09:50:41Z
has_accepted_license: '1'
intvolume: '       325'
isi: 1
issue: '2'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 331-351
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Pacific Journal of Mathematics
publication_identifier:
  eissn:
  - 0030-8730
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Some effectivity results for primitive divisors of elliptic divisibility  sequences
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 325
year: '2023'
...
---
_id: '12311'
abstract:
- lang: eng
  text: "In this note we prove a formula for the cancellation exponent $k_{v,n}$ between
    division polynomials $\\psi_n$ and $\\phi_n$ associated with a sequence $\\{nP\\}_{n\\in\\mathbb{N}}$
    of points on an elliptic curve $E$ defined over a discrete valuation field $K$.
    The formula is identical with the result of Yabuta-Voutier for the case of finite
    extension of $\\mathbb{Q}_{p}$ and\r\ngeneralizes to the case of non-standard
    Kodaira types for non-perfect residue fields."
article_number: '2203.02015'
article_processing_charge: No
arxiv: 1
author:
- first_name: Bartosz
  full_name: Naskręcki, Bartosz
  last_name: Naskręcki
- first_name: Matteo
  full_name: Verzobio, Matteo
  id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
  last_name: Verzobio
  orcid: 0000-0002-0854-0306
citation:
  ama: Naskręcki B, Verzobio M. Common valuations of division polynomials. <i>arXiv</i>.
    doi:<a href="https://doi.org/10.48550/arXiv.2203.02015">10.48550/arXiv.2203.02015</a>
  apa: Naskręcki, B., &#38; Verzobio, M. (n.d.). Common valuations of division polynomials.
    <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.2203.02015">https://doi.org/10.48550/arXiv.2203.02015</a>
  chicago: Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division
    Polynomials.” <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/arXiv.2203.02015">https://doi.org/10.48550/arXiv.2203.02015</a>.
  ieee: B. Naskręcki and M. Verzobio, “Common valuations of division polynomials,”
    <i>arXiv</i>. .
  ista: Naskręcki B, Verzobio M. Common valuations of division polynomials. arXiv,
    2203.02015.
  mla: Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.”
    <i>ArXiv</i>, 2203.02015, doi:<a href="https://doi.org/10.48550/arXiv.2203.02015">10.48550/arXiv.2203.02015</a>.
  short: B. Naskręcki, M. Verzobio, ArXiv (n.d.).
date_created: 2023-01-16T11:45:22Z
date_published: 2022-03-03T00:00:00Z
date_updated: 2023-05-08T10:42:09Z
day: '03'
doi: 10.48550/arXiv.2203.02015
extern: '1'
external_id:
  arxiv:
  - '2203.02015'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2203.02015
month: '03'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
status: public
title: Common valuations of division polynomials
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
_id: '12308'
abstract:
- lang: eng
  text: Let P and Q be two points on an elliptic curve defined over a number field
    K. For α∈End(E), define Bα to be the OK-integral ideal generated by the denominator
    of x(α(P)+Q). Let O be a subring of End(E), that is a Dedekind domain. We will
    study the sequence {Bα}α∈O. We will show that, for all but finitely many α∈O,
    the ideal Bα has a primitive divisor when P is a non-torsion point and there exist
    two endomorphisms g≠0 and f so that f(P)=g(Q). This is a generalization of previous
    results on elliptic divisibility sequences.
article_number: '37'
article_processing_charge: No
article_type: original
author:
- first_name: Matteo
  full_name: Verzobio, Matteo
  id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
  last_name: Verzobio
  orcid: 0000-0002-0854-0306
citation:
  ama: Verzobio M. Primitive divisors of sequences associated to elliptic curves with
    complex multiplication. <i>Research in Number Theory</i>. 2021;7(2). doi:<a href="https://doi.org/10.1007/s40993-021-00267-9">10.1007/s40993-021-00267-9</a>
  apa: Verzobio, M. (2021). Primitive divisors of sequences associated to elliptic
    curves with complex multiplication. <i>Research in Number Theory</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s40993-021-00267-9">https://doi.org/10.1007/s40993-021-00267-9</a>
  chicago: Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic
    Curves with Complex Multiplication.” <i>Research in Number Theory</i>. Springer
    Nature, 2021. <a href="https://doi.org/10.1007/s40993-021-00267-9">https://doi.org/10.1007/s40993-021-00267-9</a>.
  ieee: M. Verzobio, “Primitive divisors of sequences associated to elliptic curves
    with complex multiplication,” <i>Research in Number Theory</i>, vol. 7, no. 2.
    Springer Nature, 2021.
  ista: Verzobio M. 2021. Primitive divisors of sequences associated to elliptic curves
    with complex multiplication. Research in Number Theory. 7(2), 37.
  mla: Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves
    with Complex Multiplication.” <i>Research in Number Theory</i>, vol. 7, no. 2,
    37, Springer Nature, 2021, doi:<a href="https://doi.org/10.1007/s40993-021-00267-9">10.1007/s40993-021-00267-9</a>.
  short: M. Verzobio, Research in Number Theory 7 (2021).
date_created: 2023-01-16T11:44:39Z
date_published: 2021-05-20T00:00:00Z
date_updated: 2023-05-08T12:00:17Z
day: '20'
doi: 10.1007/s40993-021-00267-9
extern: '1'
intvolume: '         7'
issue: '2'
keyword:
- Algebra and Number Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1007/s40993-021-00267-9
month: '05'
oa: 1
oa_version: Published Version
publication: Research in Number Theory
publication_identifier:
  issn:
  - 2522-0160
  - 2363-9555
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Primitive divisors of sequences associated to elliptic curves with complex
  multiplication
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2021'
...
---
_id: '12309'
abstract:
- lang: eng
  text: Take a rational elliptic curve defined by the equation y2=x3+ax in minimal
    form and consider the sequence Bn of the denominators of the abscissas of the
    iterate of a non-torsion point. We show that B5m has a primitive divisor for every
    m. Then, we show how to generalize this method to the terms of the form Bmp with
    p a prime congruent to 1 modulo 4.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Matteo
  full_name: Verzobio, Matteo
  id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
  last_name: Verzobio
  orcid: 0000-0002-0854-0306
citation:
  ama: Verzobio M. Primitive divisors of elliptic divisibility sequences for elliptic
    curves with j=1728. <i>Acta Arithmetica</i>. 2021;198(2):129-168. doi:<a href="https://doi.org/10.4064/aa191016-30-7">10.4064/aa191016-30-7</a>
  apa: Verzobio, M. (2021). Primitive divisors of elliptic divisibility sequences
    for elliptic curves with j=1728. <i>Acta Arithmetica</i>. Institute of Mathematics,
    Polish Academy of Sciences. <a href="https://doi.org/10.4064/aa191016-30-7">https://doi.org/10.4064/aa191016-30-7</a>
  chicago: Verzobio, Matteo. “Primitive Divisors of Elliptic Divisibility Sequences
    for Elliptic Curves with J=1728.” <i>Acta Arithmetica</i>. Institute of Mathematics,
    Polish Academy of Sciences, 2021. <a href="https://doi.org/10.4064/aa191016-30-7">https://doi.org/10.4064/aa191016-30-7</a>.
  ieee: M. Verzobio, “Primitive divisors of elliptic divisibility sequences for elliptic
    curves with j=1728,” <i>Acta Arithmetica</i>, vol. 198, no. 2. Institute of Mathematics,
    Polish Academy of Sciences, pp. 129–168, 2021.
  ista: Verzobio M. 2021. Primitive divisors of elliptic divisibility sequences for
    elliptic curves with j=1728. Acta Arithmetica. 198(2), 129–168.
  mla: Verzobio, Matteo. “Primitive Divisors of Elliptic Divisibility Sequences for
    Elliptic Curves with J=1728.” <i>Acta Arithmetica</i>, vol. 198, no. 2, Institute
    of Mathematics, Polish Academy of Sciences, 2021, pp. 129–68, doi:<a href="https://doi.org/10.4064/aa191016-30-7">10.4064/aa191016-30-7</a>.
  short: M. Verzobio, Acta Arithmetica 198 (2021) 129–168.
date_created: 2023-01-16T11:44:54Z
date_published: 2021-01-04T00:00:00Z
date_updated: 2023-05-08T11:58:14Z
day: '04'
doi: 10.4064/aa191016-30-7
extern: '1'
external_id:
  arxiv:
  - '2001.09634'
intvolume: '       198'
issue: '2'
keyword:
- Algebra and Number Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2001.09634
month: '01'
oa: 1
oa_version: Preprint
page: 129-168
publication: Acta Arithmetica
publication_identifier:
  issn:
  - 0065-1036
  - 1730-6264
publication_status: published
publisher: Institute of Mathematics, Polish Academy of Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: Primitive divisors of elliptic divisibility sequences for elliptic curves with
  j=1728
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 198
year: '2021'
...
---
_id: '12314'
abstract:
- lang: eng
  text: "In literature, there are two different definitions of elliptic divisibility\r\nsequences.
    The first one says that a sequence of integers $\\{h_n\\}_{n\\geq 0}$\r\nis an
    elliptic divisibility sequence if it verifies the recurrence relation\r\n$h_{m+n}h_{m-n}h_{r}^2=h_{m+r}h_{m-r}h_{n}^2-h_{n+r}h_{n-r}h_{m}^2$
    for every\r\nnatural number $m\\geq n\\geq r$. The second definition says that
    a sequence of\r\nintegers $\\{\\beta_n\\}_{n\\geq 0}$ is an elliptic divisibility
    sequence if it is\r\nthe sequence of the square roots (chosen with an appropriate
    sign) of the\r\ndenominators of the abscissas of the iterates of a point on a
    rational elliptic\r\ncurve. It is well-known that the two sequences are not equivalent.
    Hence, given\r\na sequence of the denominators $\\{\\beta_n\\}_{n\\geq 0}$, in
    general does not\r\nhold\r\n$\\beta_{m+n}\\beta_{m-n}\\beta_{r}^2=\\beta_{m+r}\\beta_{m-r}\\beta_{n}^2-\\beta_{n+r}\\beta_{n-r}\\beta_{m}^2$\r\nfor
    $m\\geq n\\geq r$. We will prove that the recurrence relation above holds for\r\n$\\{\\beta_n\\}_{n\\geq
    0}$ under some conditions on the indexes $m$, $n$, and $r$."
article_number: '2102.07573'
article_processing_charge: No
arxiv: 1
author:
- first_name: Matteo
  full_name: Verzobio, Matteo
  id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
  last_name: Verzobio
  orcid: 0000-0002-0854-0306
citation:
  ama: Verzobio M. A recurrence relation for elliptic divisibility sequences. <i>arXiv</i>.
    doi:<a href="https://doi.org/10.48550/arXiv.2102.07573">10.48550/arXiv.2102.07573</a>
  apa: Verzobio, M. (n.d.). A recurrence relation for elliptic divisibility sequences.
    <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.2102.07573">https://doi.org/10.48550/arXiv.2102.07573</a>
  chicago: Verzobio, Matteo. “A Recurrence Relation for Elliptic Divisibility Sequences.”
    <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/arXiv.2102.07573">https://doi.org/10.48550/arXiv.2102.07573</a>.
  ieee: M. Verzobio, “A recurrence relation for elliptic divisibility sequences,”
    <i>arXiv</i>. .
  ista: Verzobio M. A recurrence relation for elliptic divisibility sequences. arXiv,
    2102.07573.
  mla: Verzobio, Matteo. “A Recurrence Relation for Elliptic Divisibility Sequences.”
    <i>ArXiv</i>, 2102.07573, doi:<a href="https://doi.org/10.48550/arXiv.2102.07573">10.48550/arXiv.2102.07573</a>.
  short: M. Verzobio, ArXiv (n.d.).
date_created: 2023-01-16T11:46:36Z
date_published: 2021-02-15T00:00:00Z
date_updated: 2023-02-21T10:22:57Z
day: '15'
doi: 10.48550/arXiv.2102.07573
extern: '1'
external_id:
  arxiv:
  - '2102.07573'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.2102.07573'
month: '02'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
status: public
title: A recurrence relation for elliptic divisibility sequences
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '12310'
abstract:
- lang: eng
  text: Let  be a sequence of points on an elliptic curve defined over a number field
    K. In this paper, we study the denominators of the x-coordinates of this sequence.
    We prove that, if Q is a torsion point of prime order, then for n large enough
    there always exists a primitive divisor. Later on, we show the link between the
    study of the primitive divisors and a Lang-Trotter conjecture. Indeed, given two
    points P and Q on the elliptic curve, we prove a lower bound for the number of
    primes p such that P is in the orbit of Q modulo p.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Matteo
  full_name: Verzobio, Matteo
  id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
  last_name: Verzobio
  orcid: 0000-0002-0854-0306
citation:
  ama: Verzobio M. Primitive divisors of sequences associated to elliptic curves.
    <i>Journal of Number Theory</i>. 2020;209(4):378-390. doi:<a href="https://doi.org/10.1016/j.jnt.2019.09.003">10.1016/j.jnt.2019.09.003</a>
  apa: Verzobio, M. (2020). Primitive divisors of sequences associated to elliptic
    curves. <i>Journal of Number Theory</i>. Elsevier. <a href="https://doi.org/10.1016/j.jnt.2019.09.003">https://doi.org/10.1016/j.jnt.2019.09.003</a>
  chicago: Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic
    Curves.” <i>Journal of Number Theory</i>. Elsevier, 2020. <a href="https://doi.org/10.1016/j.jnt.2019.09.003">https://doi.org/10.1016/j.jnt.2019.09.003</a>.
  ieee: M. Verzobio, “Primitive divisors of sequences associated to elliptic curves,”
    <i>Journal of Number Theory</i>, vol. 209, no. 4. Elsevier, pp. 378–390, 2020.
  ista: Verzobio M. 2020. Primitive divisors of sequences associated to elliptic curves.
    Journal of Number Theory. 209(4), 378–390.
  mla: Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves.”
    <i>Journal of Number Theory</i>, vol. 209, no. 4, Elsevier, 2020, pp. 378–90,
    doi:<a href="https://doi.org/10.1016/j.jnt.2019.09.003">10.1016/j.jnt.2019.09.003</a>.
  short: M. Verzobio, Journal of Number Theory 209 (2020) 378–390.
date_created: 2023-01-16T11:45:07Z
date_published: 2020-04-01T00:00:00Z
date_updated: 2023-05-10T11:14:56Z
day: '01'
doi: 10.1016/j.jnt.2019.09.003
extern: '1'
external_id:
  arxiv:
  - '1906.00632'
intvolume: '       209'
issue: '4'
keyword:
- Algebra and Number Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1906.00632
month: '04'
oa: 1
oa_version: Preprint
page: 378-390
publication: Journal of Number Theory
publication_identifier:
  issn:
  - 0022-314X
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Primitive divisors of sequences associated to elliptic curves
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 209
year: '2020'
...