Enhanced zeta distributions and its functional equations

Kyo Nishiyama; Bent Ørsted; Akihito Wachi

doi:10.1088/1742-6596/1194/1/012081

Enhanced zeta distributions and its functional equations

Kyo Nishiyama, Bent Ørsted, Akihito Wachi

Department of Mathematics

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Abstract

We consider an "enhanced symmetric space", which is a prehomogeneous vector space. This vector space is intimately related to a double flag variety studied in [1]. On a distinguished open orbit called "enhanced positive cone", we consider a zeta integral with two complex variables, which is analytically continued to meromorphic family of tempered distributions. One of the main results of this paper is to establish a precise formula for the meromorphic continuation which clarifies the location of poles (and may be useful to obtain residues). We also compute the Fourier transform of the zeta distribution and obtain a functional equation with explicit gamma factors.

Original language	English
Article number	012081
Book series	Journal of Physics: Conference Series
Volume	1194
Issue	1
Number of pages	11
ISSN	1742-6588
DOIs	https://doi.org/10.1088/1742-6596/1194/1/012081
Publication status	Published - 2019
Event	32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018 - Prague, Czech Republic Duration: 9 Jul 2018 → 13 Jul 2018

Conference

Conference	32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018
Country/Territory	Czech Republic
City	Prague
Period	09/07/2018 → 13/07/2018

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10.1088/1742-6596/1194/1/012081Licence: CC BY

Nishiyama_2019_J._Phys. _Conf._Ser._1194_012081Final published version, 577 KBLicence: CC BY

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title = "Enhanced zeta distributions and its functional equations",

abstract = "We consider an {"}enhanced symmetric space{"}, which is a prehomogeneous vector space. This vector space is intimately related to a double flag variety studied in [1]. On a distinguished open orbit called {"}enhanced positive cone{"}, we consider a zeta integral with two complex variables, which is analytically continued to meromorphic family of tempered distributions. One of the main results of this paper is to establish a precise formula for the meromorphic continuation which clarifies the location of poles (and may be useful to obtain residues). We also compute the Fourier transform of the zeta distribution and obtain a functional equation with explicit gamma factors.",

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AU - Nishiyama, Kyo

AU - Ørsted, Bent

AU - Wachi, Akihito

PY - 2019

Y1 - 2019

N2 - We consider an "enhanced symmetric space", which is a prehomogeneous vector space. This vector space is intimately related to a double flag variety studied in [1]. On a distinguished open orbit called "enhanced positive cone", we consider a zeta integral with two complex variables, which is analytically continued to meromorphic family of tempered distributions. One of the main results of this paper is to establish a precise formula for the meromorphic continuation which clarifies the location of poles (and may be useful to obtain residues). We also compute the Fourier transform of the zeta distribution and obtain a functional equation with explicit gamma factors.

AB - We consider an "enhanced symmetric space", which is a prehomogeneous vector space. This vector space is intimately related to a double flag variety studied in [1]. On a distinguished open orbit called "enhanced positive cone", we consider a zeta integral with two complex variables, which is analytically continued to meromorphic family of tempered distributions. One of the main results of this paper is to establish a precise formula for the meromorphic continuation which clarifies the location of poles (and may be useful to obtain residues). We also compute the Fourier transform of the zeta distribution and obtain a functional equation with explicit gamma factors.

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DO - 10.1088/1742-6596/1194/1/012081

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AN - SCOPUS:85065563530

SN - 1742-6588

VL - 1194

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

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T2 - 32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018

Y2 - 9 July 2018 through 13 July 2018

ER -

Enhanced zeta distributions and its functional equations

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