Rankin–Selberg integrals for principal series representations of GL(n)

  title={Rankin–Selberg integrals for principal series representations of GL(n)},
  author={Dongwen Liu and Fengqiu Su and Binyong Sun},
  journal={Forum Mathematicum},
  pages={1549 - 1559}
  • Dongwen Liu, F. Su, Binyong Sun
  • Published 11 September 2021
  • Mathematics
  • Forum Mathematicum
Abstract We prove that the local Rankin–Selberg integrals for principal series representations of the general linear groups agree with certain simple integrals over the Rankin–Selberg subgroups, up to certain constants given by the local gamma factors. 


Archimedean Rankin-Selberg Integrals
The paper gives complete proofs of the properties of the Rankin- Selberg integrals for the group GL(n;R) and GL(n;C).
Real reductive groups
Intertwining operators completions of admissible (g,K)-modules the theory of the leading term the Harish-Chandra plancherel theorem abstract representation theory the Whittaker plancherel theorem.
Schwartz homologies of representations of almost linear Nash groups
Let $G$ be an almost linear Nash group, namely, a Nash group which admits a Nash homomorphism with finite kernel to some $\GL_k(\mathbb R)$. A homology theory (the Schwartz homology) is establishedExpand
Schwartz Functions on Nash Manifolds
The goal of this paper we extend the notions of Schwartz functions, tempered functions, and generalized Schwartz functions to Nash (i.e. smooth semi-algebraic) manifolds. We reprove for this case theExpand
Number Theoretic Background
This paper is an expanded version of some of the lectures given at the summer school in Bologna. In these lectures we gave an introduction to very basic number theory, assuming practically noExpand
Tate’s Thesis
Tate’s thesis, Fourier Analysis in Number Fields and Hecke’s Zeta-Functions (Princeton, 1950) first appeared in print as Chapter XV of the conference proceedings Algebraic Number Theory, edited byExpand
An introduction to the Langlands program
Preface.- E. Kowalski - Elementary Theory of L-Functions I.- E. Kowalski - Elementary Theory of L-Functions II.- E. Kowalski - Classical Automorphic Forms.- E. DeShalit - Artin L-Functions.- E.Expand
Translated from Russian by
2. In the present Basics, the Arctic zone of the Russian Federation means a part of the Arctic which includes, in full or in part, the territories of the Republic of Sakha (Yakutia), Murmansk andExpand
New Haven
Every so often, often in fall, we remember that public greens were once our burial grounds. For hanged men, poxy corpses, slaves: the other, from when the green was on the edge of town. In New Haven,Expand
Automorphic forms and L-functions II. Local aspects
  • Israel Math. Conf. Proc., Amer. Math. Soc
  • 2009