A fast algorithm to compute L(1/2, f x χq)

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JournalJournal of Number Theory
DateE-pub ahead of print - 23 Dec 2012
DatePublished (current) - May 2013
Issue number5
Volume133
Number of pages23
Pages (from-to)1502-1524
Early online date23/12/12
Original languageEnglish

Abstract

Let $f$ be a fixed (holomorphic or Maass) modular cusp form. Let $\cq$ be a Dirichlet character mod $q$. We describe a fast algorithm that computes the value $L(1/2,f\times\chi_q)$ up to any specified precision. In the case when $q$ is smooth or highly composite integer, the time complexity of the algorithm is given by $O(1+|q|^{5/6+o(1)})$.

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© 2012 Elsevier Inc. This is an author produced version of a paper published in Journal of Number Theory. Uploaded in accordance with the publisher's self-archiving policy.

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  • math.NT

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