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.References
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Additional Information
- Ghaith A. Hiary
- Affiliation: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210
- MR Author ID: 930454
- Received by editor(s): March 20, 2014
- Received by editor(s) in revised form: July 31, 2014
- Published electronically: October 15, 2015
- Additional Notes: Preparation of this material was partially supported by the National Science Foundation under agreement No. DMS-0932078 (while at MSRI) and DMS-1406190, and by the Leverhulme Trust (while at the University of Bristol).
- © Copyright 2015 American Mathematical Society
- Journal: Math. Comp. 85 (2016), 1017-1032
- MSC (2010): Primary 11M06, 11Y16; Secondary 68Q25
- DOI: https://doi.org/10.1090/mcom/3019
- MathSciNet review: 3434892