Hybrid subconvexity for class group L-functions and uniform sup norm bounds of Eisenstein series
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- Hybrid subconvexity for class group
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In this paper, we study hybrid subconvexity bounds for class group L-functions associated to quadratic extensions K/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 + it) ≪ε y1/2(|t| + 1)1/3+ε, y ≫ 1, extending work of Blomer and Titchmarsh. Finally, we propose a uniform version of the sup norm conjecture for Eisenstein series.
Original language | English |
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Journal | Forum Mathematicum |
Volume | 33 |
Issue number | 1 |
Pages (from-to) | 39-57 |
ISSN | 0933-7741 |
DOIs | |
Publication status | Published - 2021 |
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