Explicit conditional bounds for the residue of a Dedekind zeta-function at s=1

2025/06/20 by Stephan Ramon Garcia, Garcia, Stephan Ramon, Grenié, Loïc +2
Mathematics · #11M06 #11M99 #11R42 #11S40 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2506.17416

openalex publication_date 2025/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove new explicit conditional bounds for the residue at s=1 of the Dedekind zeta-function associated to a number field. Our bounds are concrete and all constants are presented with explicit numerical values.

Citations

• On Turing's method for Artin L-functions and the Selberg class
• Sharper bounds for the error in the prime number theorem assuming the Riemann Hypothesis
• Conditional estimates for L-functions in the Selberg class
• Explicit estimates for Artin L-functions: Duke's short-sum theorem and\n Dedekind Zeta Residues
• A bias in Mertens' product formula
• Large character sums
• Approximate formulas for some functions of prime numbers

Related

• Computing the residue of the Dedekind zeta function
• On the lowest zero of Dedekind zeta function
• New zero-free regions for Dedekind zeta-functions at small and large ordinates
• On Diophantine properties for values of Dedekind zeta functions
• Sharp Upper Bounds for Moments of Dedekind Zeta Functions