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arXiv · 1211.4181

Evaluating $L$-functions with few known coefficients

David W. Farmer·Nathan C. Ryan
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Abstract

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 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.

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David W. Farmer, Nathan C. Ryan. 2012-11-18. Evaluating $L$-functions with few known coefficients. https://doi.org/10.1112/s1461157013000314

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