Consequences of the Gross–Zagier formulae: Stability of average L-values, subconvexity, and non-vanishing mod p

DOI10.1007/978-1-4614-1260-1_20zbMath1276.11057arXiv0709.4668OpenAlexW1582499994MaRDI QIDQ2914179

Dinakar Ramakrishnan, Philippe Michel

Publication date: 25 September 2012

Published in: Number Theory, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.4668

zbMATH Keywords

stabilitysubconvexitynon-vanishingaverage \(L\)-valuesGross-Zagier formulae

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11) Automorphic forms, one variable (11F12)

Related Items (13)

Hecke-Maass cusp forms on \(\operatorname{PGL}_n\) of large levels with non-vanishing \(L\)-values ⋮ Rankin-Selberg \(L\)-functions and the reduction of CM elliptic curves ⋮ Test vectors and central \(L\)-values for \(\mathrm{GL}(2)\) ⋮ AVERAGES OF TWISTED -FUNCTIONS ⋮ First moment of Rankin-Selberg central \(L\)-values and subconvexity in the level aspect ⋮ Stable averages of central values of Rankin-Selberg \(L\)-functions: some new variants ⋮ Weighted Distribution of Low-lying Zeros of GL(2) -functions ⋮ Modular degrees of elliptic curves and some quotient of \(L\)-values ⋮ Hybrid bounds for Rankin-Selberg \(L\)-functions ⋮ On tensor product \(L\)-functions for quaternion unitary groups and \(\mathrm{GL}(2)\) over totally real number fields: mixed weight cases ⋮ Relative trace formulas and subconvexity estimates for $L$-functions of Hilbert modular forms ⋮ Rational points on twisted modular curves ⋮ Exact double averages of twisted \(L\)-values

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