An alternative to Riemann-Siegel type formulas

Hiary, Ghaith

doi:10.1090/mcom/3019

An alternative to Riemann-Siegel type formulas
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by Ghaith A. Hiary PDF

Math. Comp. 85 (2016), 1017-1032 Request permission

Abstract:

Simple unsmoothed formulas to compute the Riemann zeta function, and Dirichlet $L$-functions to a powerfull modulus, are derived by elementary means (Taylor expansions and the geometric series). The formulas enable the square-root of the analytic conductor complexity, up to logarithmic loss, and have an explicit remainder term that is easy to control. The formula for zeta yields a convexity bound of the same strength as that from the Riemann-Siegel formula, up to a constant factor. Practical parameter choices are discussed.

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