Absolutely simple polarized abelian varieties of odd Sophie Germain prime dimension over finite fields with maximal automorphism groups

Won Tae Hwang; Kyunghwan Song

doi:10.1016/j.jnt.2020.12.003

Absolutely simple polarized abelian varieties of odd Sophie Germain prime dimension over finite fields with maximal automorphism groups

Won Tae Hwang^*
, Kyunghwan Song

^*Corresponding author for this work

Department of Mathematics

Korea Institute for Advanced Study

Research output: Contribution to journal › Journal article › peer-review

Abstract

For each Sophie Germain prime g≥5, we construct an absolutely simple polarized abelian variety of dimension g over a finite field, whose automorphism group is a cyclic group of order 4g+2. We also provide a description on the asymptotic behavior of prime numbers that are related to our construction.

Original language	English
Pages (from-to)	262-277
Number of pages	16
Journal	Journal of Number Theory
Volume	222
DOIs	https://doi.org/10.1016/j.jnt.2020.12.003
State	Published - 2021.05

Keywords

Absolutely simple polarized abelian varieties over finite fields
Automorphism groups
Distribution of primes

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10.1016/j.jnt.2020.12.003

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@article{ff70d4a542a741c187c251356e75b186,

title = "Absolutely simple polarized abelian varieties of odd Sophie Germain prime dimension over finite fields with maximal automorphism groups",

abstract = "For each Sophie Germain prime g≥5, we construct an absolutely simple polarized abelian variety of dimension g over a finite field, whose automorphism group is a cyclic group of order 4g+2. We also provide a description on the asymptotic behavior of prime numbers that are related to our construction.",

keywords = "Absolutely simple polarized abelian varieties over finite fields, Automorphism groups, Distribution of primes",

author = "Hwang, \{Won Tae\} and Kyunghwan Song",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2021",

month = may,

doi = "10.1016/j.jnt.2020.12.003",

language = "English",

volume = "222",

pages = "262--277",

journal = "Journal of Number Theory",

issn = "0022-314X",

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TY - JOUR

T1 - Absolutely simple polarized abelian varieties of odd Sophie Germain prime dimension over finite fields with maximal automorphism groups

AU - Hwang, Won Tae

AU - Song, Kyunghwan

PY - 2021/5

Y1 - 2021/5

N2 - For each Sophie Germain prime g≥5, we construct an absolutely simple polarized abelian variety of dimension g over a finite field, whose automorphism group is a cyclic group of order 4g+2. We also provide a description on the asymptotic behavior of prime numbers that are related to our construction.

AB - For each Sophie Germain prime g≥5, we construct an absolutely simple polarized abelian variety of dimension g over a finite field, whose automorphism group is a cyclic group of order 4g+2. We also provide a description on the asymptotic behavior of prime numbers that are related to our construction.

KW - Absolutely simple polarized abelian varieties over finite fields

KW - Automorphism groups

KW - Distribution of primes

UR - https://www.scopus.com/pages/publications/85100221692

U2 - 10.1016/j.jnt.2020.12.003

DO - 10.1016/j.jnt.2020.12.003

M3 - Journal article

AN - SCOPUS:85100221692

SN - 0022-314X

VL - 222

SP - 262

EP - 277

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Absolutely simple polarized abelian varieties of odd Sophie Germain prime dimension over finite fields with maximal automorphism groups

Abstract

Keywords

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