Prime Distribution and Siegel Zeroes

2023/11/21 by Thomas Wright, Wright, Thomas · 2 citations
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2311.12470

openalex publication_date 2023/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let χ be a Dirichlet character mod D with L(s,χ) its associated L-function, and let ψ(x,q,a) be, as usual, Chebyshev's prime-counting function for the primes of the arithmetic progression a (mod q) with (a,q)=1. For a fixed R>7, we prove that under the assumption of an exceptional character χ with L(1,χ)<(log D)^-R, there exists a range of x for which the asymptotic ψ(x,q,a)=(ψ(x))/(ϕ(q))(1-χ((aD)/((q,D)))+o(1)) holds for q

Cited by

• Primes in arithmetic progressions under the presence of Landau-Siegel zeroes
• Primes in Arithmetic Progressions to Large Moduli and Siegel Zeroes

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