Enhanced zeta distributions and its functional equations

TY - GEN

T1 - Enhanced zeta distributions and its functional equations

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.

UR - http://www.scopus.com/inward/record.url?scp=85065563530&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1194/1/012081

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

M3 - Conference article

AN - SCOPUS:85065563530

SN - 1742-6588

VL - 1194

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012081

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

Y2 - 9 July 2018 through 13 July 2018

ER -