Lower order terms of the second moment of S(t)

2004/11/22 by Tsz Ho Chan, Chan, Tsz Ho
Mathematics · #11M06 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #math.NT #msc:11M06

paper · pdf · doi:10.48550/arxiv.math/0411501

19 pages

arxiv created 2004/11/22 · openalex publication_date 2004/11/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we derive an asymptotic formula for the second moment of S(t) which includes the lower order terms using a prediction from the ratios conjecture of Conrey, Farmer and Zirnbauer. The formula matches very well with actual values of the second moment.

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