Rapid computation of L-functions attached to Maass forms

Andrew R Booker; Holger L Then

doi:10.1142/S1793042118500896

Rapid computation of L-functions attached to Maass forms

Andrew R Booker^*, Holger L Then

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

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Abstract

Let L be a degree-2 L-function associated to a Maass cusp form.We explore an algorithm that evaluates t values of L on the critical line in time O(t1+ε). We use this algorithm to rigorously compute an abundance of consecutive zeros and investigate their distribution.

Original language	English
Pages (from-to)	1459-1485
Number of pages	27
Journal	International Journal of Number Theory
Volume	14
Issue number	5
Early online date	19 Jan 2018
DOIs	https://doi.org/10.1142/S1793042118500896
Publication status	Published - Jun 2018

Keywords

L-functions
automorphic forms

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10.1142/S1793042118500896

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via World Scientific at http://www.worldscientific.com/doi/abs/10.1142/S1793042118500896 . Please refer to any applicable terms of use of the publisher.
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title = "Rapid computation of L-functions attached to Maass forms",

abstract = "Let L be a degree-2 L-function associated to a Maass cusp form.We explore an algorithm that evaluates t values of L on the critical line in time O(t1+ε). We use this algorithm to rigorously compute an abundance of consecutive zeros and investigate their distribution.",

keywords = "L-functions, automorphic forms",

author = "Booker, {Andrew R} and Then, {Holger L}",

year = "2018",

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journal = "International Journal of Number Theory",

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TY - JOUR

T1 - Rapid computation of L-functions attached to Maass forms

AU - Booker, Andrew R

AU - Then, Holger L

PY - 2018/6

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N2 - Let L be a degree-2 L-function associated to a Maass cusp form.We explore an algorithm that evaluates t values of L on the critical line in time O(t1+ε). We use this algorithm to rigorously compute an abundance of consecutive zeros and investigate their distribution.

AB - Let L be a degree-2 L-function associated to a Maass cusp form.We explore an algorithm that evaluates t values of L on the critical line in time O(t1+ε). We use this algorithm to rigorously compute an abundance of consecutive zeros and investigate their distribution.

KW - L-functions

KW - automorphic forms

UR - http://www.scopus.com/inward/record.url?scp=85040684366&partnerID=8YFLogxK

UR - https://arxiv.org/abs/1703.08863

U2 - 10.1142/S1793042118500896

DO - 10.1142/S1793042118500896

M3 - Article (Academic Journal)

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SP - 1459

EP - 1485

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 5

ER -

Rapid computation of L-functions attached to Maass forms

Abstract

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Explicit number theory, automorphic forms and L-functions

Cite this

Rapid computation of L-functions attached to Maass forms

Abstract

Keywords

Access to Document

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Other files and links

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Projects

Explicit number theory, automorphic forms and L-functions

Cite this