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Explicit Burgess-like subconvex bounds for GL2 × GL1

Published/Copyright: July 16, 2020
Forum Mathematicum
From the journal Forum Mathematicum Volume 32 Issue 5

Abstract

We make the polynomial dependence on the fixed representation π in our previous subconvex bound of L⁢(12,π⊗χ) for GL2×GL1 explicit, especially in terms of the usual conductor 𝐂⁢(πfin). There is no clue that the original choice, due to Michel and Venkatesh, of the test function at the infinite places should be the optimal one. Hence we also investigate a possible variant of such local choices in some special situations.

Keywords: Subconvexity; twisted L-function
MSC 2010: 11M41

Communicated by Jan Bruinier

Funding source: Leverhulme Trust

Award Identifier / Grant number: RPG-2018-401

Funding statement: The preparation of the paper scattered during the stays of the author’s in FIM at ETHZ, at Alféd Renyi Institute in Hungary supported by the MTA Rényi Intézet Lendület Automorphic Research Group, in TAN at EPFL and in the School of Mathematical Sciences at Queen Mary University of London. The author would like to thank these institutes for their hospitality, and the support of the Leverhulme Trust Research Project Grant RPG-2018-401.

Acknowledgements

The author would like to thank the referee for careful reading.

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Received: 2019-03-26
Revised: 2020-02-13
Published Online: 2020-07-16
Published in Print: 2020-09-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Conjugacy classes and automorphisms of twin groups
  3. Decomposition and classification of length functions
  4. Successive coefficients of close-to-convex functions
  5. Frobenius cowreaths and Morita contexts
  6. The non-linear sewing lemma III: Stability and generic properties
  7. On hyperquadrics containing projective varieties
  8. Explicit Burgess-like subconvex bounds for GL2 × GL1
  9. Characterisation of polyhedral products with finite generalised Postnikov decomposition
  10. Solvable Lie and Leibniz superalgebras with a given nilradical
  11. Alvis–Curtis duality for representations of reductive groups with Frobenius maps
  12. The third partial cohomology group and existence of extensions of semilattices of groups by groups
  13. Instanton bundles on two Fano threefolds of index 1
  14. Carleson measure characterizations of the Campanato type space associated with Schrödinger operators on stratified Lie groups
https://doi.org/10.1515/forum-2019-0074
Keywords for this article
Subconvexity; twisted L-function

Articles in the same Issue

  1. Frontmatter
  2. Conjugacy classes and automorphisms of twin groups
  3. Decomposition and classification of length functions
  4. Successive coefficients of close-to-convex functions
  5. Frobenius cowreaths and Morita contexts
  6. The non-linear sewing lemma III: Stability and generic properties
  7. On hyperquadrics containing projective varieties
  8. Explicit Burgess-like subconvex bounds for GL2 × GL1
  9. Characterisation of polyhedral products with finite generalised Postnikov decomposition
  10. Solvable Lie and Leibniz superalgebras with a given nilradical
  11. Alvis–Curtis duality for representations of reductive groups with Frobenius maps
  12. The third partial cohomology group and existence of extensions of semilattices of groups by groups
  13. Instanton bundles on two Fano threefolds of index 1
  14. Carleson measure characterizations of the Campanato type space associated with Schrödinger operators on stratified Lie groups
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