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Uniform asymptotics for the full moment conjecture of the Riemann zeta function
- Source :
-
Journal of Number Theory . Apr2012, Vol. 132 Issue 4, p820-868. 49p. - Publication Year :
- 2012
-
Abstract
- Abstract: Conrey, Farmer, Keating, Rubinstein, and Snaith, recently conjectured formulas for the full asymptotics of the moments of L-functions. In the case of the Riemann zeta function, their conjecture states that the 2k-th absolute moment of zeta on the critical line is asymptotically given by a certain 2k-fold residue integral. This residue integral can be expressed as a polynomial of degree , whose coefficients are given in exact form by elaborate and complicated formulas. In this article, uniform asymptotics for roughly the first k coefficients of the moment polynomial are derived. Numerical data to support our asymptotic formula are presented. An application to bounding the maximal size of the zeta function is considered. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 132
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 71489555
- Full Text :
- https://doi.org/10.1016/j.jnt.2011.09.009