Archimedean Theory and đťś–-Factors for the Asai Rankin-Selberg Integrals

2021 ◽  
pp. 1-50
Author(s):  
Raphaël Beuzart-Plessis
Keyword(s):  
Selberg Integrals

RANKIN–SELBERG INTEGRALS FOR LOCAL SYMMETRIC SQUARE FACTORS ON GL(2)

Mathematika ◽  
10.1112/mtk.12079 ◽  
2021 ◽  
Vol 67 (2) ◽  
pp. 388-421
Author(s):  
Yeongseong Jo
Keyword(s):  
Selberg Integrals ◽  
Symmetric Square

Multiplicativity of the gamma factors of Rankin–Selberg integrals for SO 2l × GL n

2012 ◽  
Vol 142 (3-4) ◽  
pp. 307-346 ◽  
Author(s):  
Eyal Kaplan
Keyword(s):  
Selberg Integrals

scholarly journals Selberg integrals, super-hypergeometric functions and applications to β-ensembles of random matrices

2015 ◽  
Vol 04 (02) ◽  
pp. 1550007 ◽  
Author(s):  
Patrick Desrosiers ◽  
Dang-Zheng Liu
Keyword(s):  
Hypergeometric Functions ◽  
Matrix Theory ◽  
Direct Application ◽  
Holonomic System ◽  
Expectation Value ◽  
Linear Partial Differential Equations ◽  
Integral Formulas ◽  
Duality Relations ◽  
Selberg Integrals ◽  
Type Integral

We study a new Selberg-type integral with n + m indeterminates, which turns out to be related to the deformed Calogero–Sutherland systems. We show that the integral satisfies a holonomic system of n + m non-symmetric linear partial differential equations. We also prove that a particular hypergeometric function defined in terms of super-Jack polynomials is the unique solution of the system. Some properties such as duality relations, integral formulas, Pfaff–Euler and Kummer transformations are also established. As a direct application, we evaluate the expectation value of ratios of characteristic polynomials in the classical β-ensembles of Random Matrix Theory.

scholarly journals Periods of automorphic forms: the case of

Compositio Mathematica ◽  
2014 ◽  
Vol 151 (4) ◽  
pp. 665-712 ◽  
Author(s):  
Atsushi Ichino ◽  
Shunsuke Yamana
Keyword(s):  
Automorphic Form ◽  
Automorphic Forms ◽  
Selberg Integral ◽  
Selberg Integrals ◽  
Diagonal Subgroup ◽  
Periods Of Automorphic Forms

Following Jacquet, Lapid and Rogawski, we define a regularized period of an automorphic form on $\text{GL}_{n+1}\times \text{GL}_{n}$ along the diagonal subgroup $\text{GL}_{n}$ and express it in terms of the Rankin–Selberg integral of Jacquet, Piatetski-Shapiro and Shalika. This extends the theory of Rankin–Selberg integrals to all automorphic forms on $\text{GL}_{n+1}\times \text{GL}_{n}$.

The unramified computation of Rankin-Selberg integrals for SO 2l Ă— GL n

2011 ◽  
Vol 191 (1) ◽  
pp. 137-184 ◽  
Author(s):  
Eyal Kaplan
Keyword(s):  
Selberg Integrals

Rankin-Selberg Integrals for the Group G 2

10.2307/2374763 ◽  
1992 ◽  
Vol 114 (6) ◽  
pp. 1269 ◽  
Author(s):  
I. Piatetski-Shapiro ◽  
S. Rallis ◽  
G. Schiffmann
Keyword(s):  
Selberg Integrals

scholarly journals Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory

Nuclear Physics B ◽  
2011 ◽  
Vol 847 (2) ◽  
pp. 413-459 ◽  
Author(s):  
M.A. Bershtein ◽  
V.A. Fateev ◽  
A.V. Litvinov
Keyword(s):  
Field Theory ◽  
Correlation Function ◽  
Selberg Integrals ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Liouville Field Theory
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