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

Pankaj Vishe

doi:10.1016/j.jnt.2012.10.005

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

Pankaj Vishe

Mathematics

Research output: Contribution to journal › Article › peer-review

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 $O(1+|q|^{5/6+o(1)})$.

Original language	English
Pages (from-to)	1502-1524
Number of pages	23
Journal	Journal of Number Theory
Volume	133
Issue number	5
Early online date	23 Dec 2012
DOIs	https://doi.org/10.1016/j.jnt.2012.10.005
Publication status	Published - May 2013

Bibliographical note

Keywords

math.NT

Access to Document

10.1016/j.jnt.2012.10.005

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Cite this

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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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