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

Abstract

For each Sophie Germain prime $g\ge 5,$ 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.

13 pages. arXiv admin note: substantial text overlap with arXiv:2002.05535, arXiv:1901.04470, arXiv:1809.06251