A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman

AR Booker

A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman

AR Booker

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

10 Citations (Scopus)

Abstract

We present a numerical test for determining whether a given set of numbers is the set of Fourier coefficients of a Maass form, without knowing its eigenvalue. Our method extends directly to consideration of holomorphic newforms. The test is applied to show that the Kloosterman sums +/-S(1, 1;p)/rootP are not the coefficients of a Maass form with small level and eigenvalue. Source code and the calculated Kloosterman sums are available electronically.

Translated title of the contribution	A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman
Original language	English
Pages (from-to)	571 - 581
Number of pages	11
Journal	Experimental Mathematics
Volume	9 (4)
Publication status	Published - 2000

Bibliographical note

Publisher: A K Peters Ltd
Other identifier: IDS number 393JJ

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title = "A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman",

abstract = "We present a numerical test for determining whether a given set of numbers is the set of Fourier coefficients of a Maass form, without knowing its eigenvalue. Our method extends directly to consideration of holomorphic newforms. The test is applied to show that the Kloosterman sums +/-S(1, 1;p)/rootP are not the coefficients of a Maass form with small level and eigenvalue. Source code and the calculated Kloosterman sums are available electronically.",

author = "AR Booker",

note = "Publisher: A K Peters Ltd Other identifier: IDS number 393JJ",

year = "2000",

language = "English",

volume = "9 (4)",

pages = "571 -- 581",

journal = "Experimental Mathematics",

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T1 - A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman

AU - Booker, AR

N1 - Publisher: A K Peters Ltd Other identifier: IDS number 393JJ

PY - 2000

Y1 - 2000

N2 - We present a numerical test for determining whether a given set of numbers is the set of Fourier coefficients of a Maass form, without knowing its eigenvalue. Our method extends directly to consideration of holomorphic newforms. The test is applied to show that the Kloosterman sums +/-S(1, 1;p)/rootP are not the coefficients of a Maass form with small level and eigenvalue. Source code and the calculated Kloosterman sums are available electronically.

AB - We present a numerical test for determining whether a given set of numbers is the set of Fourier coefficients of a Maass form, without knowing its eigenvalue. Our method extends directly to consideration of holomorphic newforms. The test is applied to show that the Kloosterman sums +/-S(1, 1;p)/rootP are not the coefficients of a Maass form with small level and eigenvalue. Source code and the calculated Kloosterman sums are available electronically.

M3 - Article (Academic Journal)

SN - 1944-950X

VL - 9 (4)

SP - 571

EP - 581

JO - Experimental Mathematics

JF - Experimental Mathematics

ER -

A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman

Abstract

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