Special value formula for the twisted triple product L-function and an application to the restricted L 2-norm problem-Reference-Cited by-同舟云学术

Special value formula for the twisted triple product L-function and an application to the restricted L 2-norm problem

Published:2020-10-10 Issue:1 Volume:33 Page:59-108
ISSN:1435-5337
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Cheng Yao¹

Affiliation:

1. Institute of Mathematics , Academia Sinica , 6F, Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road , Taipei 106319 , Taiwan

Abstract

Abstract We establish explicit Ichino’s formulae for the central values of the triple product L-functions with emphasis on the calculations for the real place. The key ingredient for our computations is Proposition 8 which generalizes a result in [P. Michel and A. Venkatesh, The subconvexity problem for GL 2

{\rm GL}_{2}

, Publ. Math. Inst. Hautes Études Sci. 111 2010, 171–271]. As an application we prove the optimal upper bound of a sum of restricted L 2

{L^{2}}

-norms of the L 2

{L^{2}}

-normalized newforms on certain quadratic extensions with prime level and bounded spectral parameter following the methods in [V. Blomer, On the 4-norm of an automorphic form, J. Eur. Math. Soc. (JEMS) 15 2013, 5, 1825–1852].

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2018-0292/pdf

Reference68 articles.

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4. V. Blomer, Subconvexity for twisted L-functions on GL⁢(3){\rm GL}(3), Amer. J. Math. 134 (2012), no. 5, 1385–1421.

5. V. Blomer, On the 4-norm of an automorphic form, J. Eur. Math. Soc. (JEMS) 15 (2013), no. 5, 1825–1852.

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