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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.


Base change and triple product $L$-series
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by Ming-Lun Hsieh and Shunsuke Yamana
Represent. Theory 26 (2022), 402-431
Published electronically: March 25, 2022


Let $\pi _i$ be an irreducible cuspidal automorphic representation of $\mathrm {GL}_2$ with central character $\omega _i$. When $\omega _1\omega _2\omega _3$ is trivial, Atsushi Ichino proved a formula for the central value $L(\frac {1}{2}, \pi _1\times \pi _2\times \pi _3)$ of the triple product $L$-series in terms of global trilinear forms. We will extend this formula to the case when $\omega _1\omega _2\omega _3$ is a quadratic character, giving a non-vanishing criterion of a local trilinear form in terms of the central value of the gamma factor.
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Bibliographic Information
  • Ming-Lun Hsieh
  • Affiliation: Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan
  • MR Author ID: 904717
  • ORCID: 0000-0002-7329-5167
  • Email:
  • Shunsuke Yamana
  • Affiliation: Osaka City University, Advanced Mathematical Institute, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
  • MR Author ID: 871756
  • Email:
  • Received by editor(s): March 17, 2020
  • Received by editor(s) in revised form: March 23, 2021
  • Published electronically: March 25, 2022
  • Additional Notes: The first author was partially supported by a MOST grants 108-2628-M-001-009-MY4 and 110-2628-M-001-004-. The second author was partially supported by JSPS Grant-in-Aid for Scientific Research (C)18K03210 and (B)19H01778. This work was partially supported by Osaka City University Advanced Mathematical Institute (MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics).
    The second author is the corresponding author
  • © Copyright 2022 American Mathematical Society
  • Journal: Represent. Theory 26 (2022), 402-431
  • MSC (2020): Primary 11F67, 11F70, 11F27
  • DOI:
  • MathSciNet review: 4400091