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Evaluating $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}L$-functions with few known coefficients

Published online by Cambridge University Press:  01 June 2014

David W. Farmer
Affiliation:
American Institute of Mathematics, 360 Portage Ave, Palo Alto, CA 94306, USA email farmer@aimath.org
Nathan C. Ryan
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA email nathan.ryan@bucknell.edu

Abstract

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We address the problem of evaluating an $L$-function when only a small number of its Dirichlet coefficients are known. We use the approximate functional equation in a new way and find that it is possible to evaluate the $L$-function more precisely than one would expect from the standard approach. The method, however, requires considerably more computational effort to achieve a given accuracy than would be needed if more Dirichlet coefficients were available.

Type
Research Article
Copyright
© The Author(s) 2014 

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