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An Asymptotic Form for the Stieltjes Constants (Gamma K)(A) and for A Sum S(Gamma)(N) Appearing Under the Li Criterion

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Title: An Asymptotic Form for the Stieltjes Constants (Gamma K)(A) and for A Sum S(Gamma)(N) Appearing Under the Li Criterion
Author(s): Knessl, Charles; Coffey, Mark W.
Subject(s): Li criterion Riemann hypothesis Stieltjes constants Hurwitz zeta function Riemann zeta function Laurent expansion asymptotic form
Abstract: We present several asymptotic analyses for quantities associated with the Riemann and Hurwitz zeta functions. We first determine the leading asymptotic behavior of the Stieltjes constants γk(a). These constants appear in the regular part of the Laurent expansion of the Hurwitz zeta function. We then use asymptotic results for the Laguerre polynomials Lαn to investigate a certain sum Sγ(n) involving the constants γk(1) that appears in application of the Li criterion for the Riemann hypothesis. We confirm the sublinear growth of Sγ(n)+n, which is consistent with the validity of the Riemann hypothesis.
Issue Date: 2011-10
Publisher: American Mathematical Society
Citation Info: Knessl, C. & Coffey, M. W. 2011. An Asymptotic Form for the Stieltjes Constants (Gamma K)(A) and for A Sum S(Gamma)(N) Appearing Under the Li Criterion. Mathematics of Computation, 80(276): 2197-2217.
Type: Article
Description: First published in Mathematics of Computation in Volume 80, Number 276 (October 2011) published by the American Mathematical Society
URI: http://hdl.handle.net/10027/8326
ISSN: 0025-5718
Sponsor: NSA Grant Number: H 98230-08-1-0102
Date Available in INDIGO: 2012-05-26
 

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