Upper bounds for |L(1,chi)|

2001/06/20 by Andrew Granville, K. Soundararajan, Granville, Andrew +2
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0106176

22 pages

arxiv created 2001/06/20 · openalex publication_date 2001/06/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a non-principal Dirichlet character chi mod q, an important problem in number theory is to obtain good estimates for the size of L(1,chi). In this paper we focus on sharpening the upper bounds known for |L(1,chi)|; in particular, we wish to determine constants c (as small as possible) for which the bound |L(1,chi)| <= (c+o(1)) log q holds.

Related

• An explicit upper bound for L(1, χ) when χ is quadratic
• Refined Upper Bounds for L(1,χ)
• The distribution of values of L(1,chi_d)
• Explicit lower bounds on |L(1, χ)|
• Explicit bounds for small prime nonresidues