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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Base change and triple product $L$-series
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by Ming-Lun Hsieh and Shunsuke Yamana PDF
Represent. Theory 26 (2022), 402-431 Request permission


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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Additional 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