Exponential decay in the frequency of analytic ranks of automorphic \(L\)-functions

DOI10.1215/S0012-7094-00-10235-9zbMath1166.11326OpenAlexW2058243336WikidataQ57268252 ScholiaQ57268252MaRDI QIDQ1567173

D. R. Heath-Brown, Philippe Michel

Publication date: 19 May 2003

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.dmj/1092749339

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36)

Related Items (4)

Families of \(L\)-functions of automorphic forms and applications ⋮ Real zeros and size of Rankin-Selberg \(L\)-functions in the level aspect ⋮ Rankin-Selberg \(L\)-functions in the level aspect. ⋮ The Second Moment Theory of Families of 𝐿-Functions–The Case of Twisted Hecke 𝐿-Functions

Cites Work

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• The size of Selmer groups for the congruent number problem
• The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky.
• Nonvanishing of quadratic Dirichlet \(L\)-functions at \(s=\frac{1}{2}\)
• The analytic rank of \(J_0(q)\) and zeros of automorphic \(L\)-functions.
• Non-vanishing of high derivatives of automorphic L-functions at the center of the critical strip

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