Twisted mellin transforms of a real analytic residue of siegeleisenstein series of degree 2

Yasuko Hasegawa; Takuya Miyazaki

doi:10.1142/S0129167X09005625

Twisted mellin transforms of a real analytic residue of siegeleisenstein series of degree 2

Yasuko Hasegawa, Takuya Miyazaki

Department of Mathematics

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

2 Citations (Scopus)

Abstract

We study a residual form of a real analytic SiegelEisenstein series, which generates a certain derived functor module occurring in a degenerate principal series representation. We compute its Mellin transforms twisted by various Maass wave forms to get explicit formulas as our results. We apply them to prove meromorphic continuations together with functional equations which are satisfied by those twisted Mellin transforms.

Original language	English
Pages (from-to)	1011-1027
Number of pages	17
Journal	International Journal of Mathematics
Volume	20
Issue number	8
DOIs	https://doi.org/10.1142/S0129167X09005625
Publication status	Published - 2009 Aug

Keywords

Confluent hypergeometric functions on tube domains
Dirichlet series
Mellin transforms
Residues of siegeleisenstein series

ASJC Scopus subject areas

Mathematics(all)

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10.1142/S0129167X09005625

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abstract = "We study a residual form of a real analytic SiegelEisenstein series, which generates a certain derived functor module occurring in a degenerate principal series representation. We compute its Mellin transforms twisted by various Maass wave forms to get explicit formulas as our results. We apply them to prove meromorphic continuations together with functional equations which are satisfied by those twisted Mellin transforms.",

keywords = "Confluent hypergeometric functions on tube domains, Dirichlet series, Mellin transforms, Residues of siegeleisenstein series",

author = "Yasuko Hasegawa and Takuya Miyazaki",

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AU - Hasegawa, Yasuko

AU - Miyazaki, Takuya

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AB - We study a residual form of a real analytic SiegelEisenstein series, which generates a certain derived functor module occurring in a degenerate principal series representation. We compute its Mellin transforms twisted by various Maass wave forms to get explicit formulas as our results. We apply them to prove meromorphic continuations together with functional equations which are satisfied by those twisted Mellin transforms.

KW - Confluent hypergeometric functions on tube domains

KW - Dirichlet series

KW - Mellin transforms

KW - Residues of siegeleisenstein series

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Twisted mellin transforms of a real analytic residue of siegeleisenstein series of degree 2

Abstract

Keywords

ASJC Scopus subject areas

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