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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Calculus of archimedean Rankin–Selberg integrals with recurrence relations
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by Taku Ishii and Tadashi Miyazaki
Represent. Theory 26 (2022), 714-763
Published electronically: July 6, 2022


Let $n$ and $n’$ be positive integers such that $n-n’\in \{0,1\}$. Let $F$ be either $\mathbb {R}$ or $\mathbb {C}$. Let $K_n$ and $K_{n’}$ be maximal compact subgroups of $\mathrm {GL}(n,F)$ and $\mathrm {GL}(n’,F)$, respectively. We give the explicit descriptions of archimedean Rankin–Selberg integrals at the minimal $K_n$- and $K_{n’}$-types for pairs of principal series representations of $\mathrm {GL}(n,F)$ and $\mathrm {GL}(n’,F)$, using their recurrence relations. Our results for $F=\mathbb {C}$ can be applied to the arithmetic study of critical values of automorphic $L$-functions.
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Bibliographic Information
  • Taku Ishii
  • Affiliation: Faculty of Science and Technology, Seikei University, 3-3-1 Kichijoji-kitamachi, Musashino, Tokyo 180-8633, Japan
  • MR Author ID: 695361
  • Email:
  • Tadashi Miyazaki
  • Affiliation: Department of Mathematics, College of Liberal Arts and Sciences, Kitasato University, 1-15-1 Kitasato, Minamiku, Sagamihara, Kanagawa 252-0373, Japan
  • MR Author ID: 854974
  • ORCID: 0000-0002-0918-8068
  • Email:
  • Received by editor(s): December 23, 2021
  • Received by editor(s) in revised form: April 8, 2022, and April 19, 2022
  • Published electronically: July 6, 2022
  • Additional Notes: This work was supported by JSPS KAKENHI Grant Numbers JP19K03452, JP18K03252
  • © Copyright 2022 American Mathematical Society
  • Journal: Represent. Theory 26 (2022), 714-763
  • MSC (2020): Primary 11F70; Secondary 11F30
  • DOI:
  • MathSciNet review: 4448934