An alternative to Riemann-Siegel type formulas

2014/03/03 by Hiary, Ghaith A.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1403.0317

Abstract

Simple unsmoothed formulas to compute the Riemann zeta function, and Dirichlet L-functions to a power-full modulus, are derived by elementary means (Taylor expansions and the geometric series). The formulas enable 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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