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Hybrid subconvexity for class group 𝐿-functions and uniform sup norm bounds of Eisenstein series

Hybrid subconvexity for class group 𝐿-functions and uniform sup norm bounds of Eisenstein series AbstractIn this paper, we study hybrid subconvexity bounds for class group L-functions associated to quadratic extensions K/ℚ{K/\mathbb{Q}} (real or imaginary).Our proof relies on relating the class group L-functions to Eisenstein series evaluated at Heegner points using formulas due to Hecke.The main technical contribution is the uniform sup norm bound for Eisenstein series E⁢(z,1/2+i⁢t)≪εy1/2⁢(|t|+1)1/3+ε{E(z,1/2+it)\ll_{\varepsilon}y^{1/2}(\lvert t\rvert+1)^{1/3+\varepsilon}}, y≫1{y\gg 1}, extending work of Blomer and Titchmarsh.Finally, we propose a uniform version of the sup norm conjecture for Eisenstein series. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Hybrid subconvexity for class group 𝐿-functions and uniform sup norm bounds of Eisenstein series

Nordentoft, Asbjørn Christian
Forum Mathematicum , Volume 33 (1): 19 – Jan 1, 2021
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Publisher
de Gruyter
Copyright
© 2020 Walter de Gruyter GmbH, Berlin/Boston
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/forum-2019-0173
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper, we study hybrid subconvexity bounds for class group L-functions associated to quadratic extensions K/ℚ{K/\mathbb{Q}} (real or imaginary).Our proof relies on relating the class group L-functions to Eisenstein series evaluated at Heegner points using formulas due to Hecke.The main technical contribution is the uniform sup norm bound for Eisenstein series E⁢(z,1/2+i⁢t)≪εy1/2⁢(|t|+1)1/3+ε{E(z,1/2+it)\ll_{\varepsilon}y^{1/2}(\lvert t\rvert+1)^{1/3+\varepsilon}}, y≫1{y\gg 1}, extending work of Blomer and Titchmarsh.Finally, we propose a uniform version of the sup norm conjecture for Eisenstein series.

Journal

Forum Mathematicum – de Gruyter

Published: Jan 1, 2021

References

  • Bounds for modular L-functions in the level aspect
  • Geometric invariants for real quadratic fields
  • Burgess-like subconvexity for GL1\mathrm{GL}_{1}
  • Arithmetic quantum chaos
  • The subconvexity problem for Artin L-functions
  • The subconvexity problem for Artin L-functions
  • Gross-Zagier formula for GL⁢(2)\mathrm{GL}(2). II
  • On Epstein’s Zeta-Function
  • Weyl-type hybrid subconvexity bounds for twisted L-functions and Heegner points on shrinking sets
  • Class numbers of indefinite binary quadratic forms. II
  • Bounds for modular L-functions in the level aspect
  • A note on the sup norm of Eisenstein series
  • Cycle integrals of the j-function and mock modular forms
  • Sup-norm bounds for Eisenstein series
  • Explicit subconvexity for GL2{\mathrm{GL}_{2}} and some applications