Exceptional characters and prime numbers in sparse sets

Fuente: arXiv
Enregistré dans:
Détails bibliographiques
Auteur principal: Merikoski, Jori
Format: Preprint
Publié: 2021
Sujets:
Accès en ligne:
Tags: Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
_version_ 1866914838377136128
author Merikoski, Jori
author_facet Merikoski, Jori
contents We develop a lower bound sieve for primes under the (unlikely) assumption of infinitely many exceptional characters. Compared with the illusory sieve due to Friedlander and Iwaniec which produces asymptotic formulas, we show that less arithmetic information is required to prove non-trivial lower bounds. As an application of our method, assuming the existence of infinitely many exceptional characters we show that there are infinitely many primes of the form $a^2+b^8$.
format Preprint
id arxiv_https___arxiv_org_abs_2108_01355
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle Exceptional characters and prime numbers in sparse sets
Merikoski, Jori
Number Theory
We develop a lower bound sieve for primes under the (unlikely) assumption of infinitely many exceptional characters. Compared with the illusory sieve due to Friedlander and Iwaniec which produces asymptotic formulas, we show that less arithmetic information is required to prove non-trivial lower bounds. As an application of our method, assuming the existence of infinitely many exceptional characters we show that there are infinitely many primes of the form $a^2+b^8$.
title Exceptional characters and prime numbers in sparse sets
topic Number Theory
url https://arxiv.org/abs/2108.01355