Uniform asymptotics for the full moment conjecture of the Riemann zeta\n function

2011/06/21 by Ghaith A. Hiary, Michael Rubinstein, Hiary, Ghaith A. +1
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1106.4352

openalex publication_date 2011/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Conrey, Farmer, Keating, Rubinstein, and Snaith, recently conjectured\nformulas for the full asymptotics of the moments of L-functions. In the case\nof the Riemann zeta function, their conjecture states that the 2k-th absolute\nmoment of zeta on the critical line is asymptotically given by a certain\n2k-fold residue integral. This residue integral can be expressed as a\npolynomial of degree k², whose coefficients are given in exact form by\nelaborate and complicated formulas. In this article, uniform asymptotics for\nroughly the first k coefficients of the moment polynomial are derived.\nNumerical data to support our asymptotic formula are presented. An application\nto bounding the maximal size of the zeta function is considered.\n

Related

• Computing the moment polynomials of the zeta function
• Lower order terms in the full moment conjecture for the Riemann zeta function
• Moments of the Riemann zeta-function
• The 4.36-th moment of the Riemann zeta-function
• A quadratic divisor problem and moments of the Riemann zeta-function