The Spectral Kuznetsov Formula on $SL(3)$

Jack Buttcane

doi:10.1090/tran/6833

The Spectral Kuznetsov Formula on $SL(3)$

Transactions of the American Mathematical Society ◽

10.1090/tran/6833 ◽

2016 ◽

Vol 368 (9) ◽

pp. 6683-6714 ◽

Cited By ~ 6

Author(s):

Jack Buttcane

Keyword(s):

Kuznetsov Formula

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Applications of the Kuznetsov formula on GL(3)

Inventiones mathematicae ◽

10.1007/s00222-013-0454-3 ◽

2013 ◽

Vol 194 (3) ◽

pp. 673-729 ◽

Cited By ~ 10

Author(s):

Valentin Blomer

Keyword(s):

Kuznetsov Formula

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A SEMI-ADELIC KUZNETSOV FORMULA OVER NUMBER FIELDS

International Journal of Number Theory ◽

10.1142/s1793042113500498 ◽

2013 ◽

Vol 09 (07) ◽

pp. 1649-1681 ◽

Cited By ~ 5

Author(s):

PÉTER MAGA

Keyword(s):

Fourier Coefficients ◽

Critical Line ◽

Analytic Number Theory ◽

Number Fields ◽

Cusp Forms ◽

Weight Functions ◽

Weighted Sum ◽

Admissible Weight ◽

Bessel Transform ◽

Kuznetsov Formula

In this paper, we prove a semi-adelic version of the Kuznetsov formula over number fields. This formula matches a weighted sum made of Fourier coefficients of cusp forms and Eisenstein series with a weighted sum of Kloosterman sums, the latter weight function is a kind of Bessel transform of the former one. We obtain a variant which is valid over all number fields. The admissible weight functions are important in applications, they depend on the archimedean parameters of the representations and show exponential decay. The automorphic vectors are not necessarily spherical in the archimedean aspect. Such formulas are proven to be useful in analytic number theory, e.g., in the estimate of L-functions on the critical line.

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