A density theorem on automorphic $L$-functions and some applications
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Publication:5695734
DOI10.1090/S0002-9947-05-03774-8zbMath1078.11032MaRDI QIDQ5695734
Publication date: 6 October 2005
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Other Dirichlet series and zeta functions (11M41) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67)
Related Items (33)
Distribution of values of symmetric power \(L\)-functions at the edge of the critical strip ⋮ Sign changes and nonvanishing of Fourier coefficients of holomorphic cusp forms ⋮ Higher-power moments of Fourier coefficients of holomorphic cusp forms for the congruence subgroup \(\varGamma_0(N)\) ⋮ The sixth and eighth moments of Fourier coefficients of cusp forms ⋮ Deterministic comparison of Hecke eigenvalues at the primes represented by a binary quadratic form ⋮ Bounds for the Petersson norms of the pullbacks of Saito-Kurokawa lifts ⋮ The average behavior of Fourier coefficients of cusp forms over sparse sequences ⋮ Absolute values of \(L\)-functions for \(\mathrm{GL}(n, \mathbb{R})\) at the point 1 ⋮ Unnamed Item ⋮ Some density results on sets of primes for Hecke eigenvalues ⋮ Values of automorphic \(L\)-functions with prime power level at the point \(s=1\) ⋮ The cancellation of Fourier coefficients of cusp forms over different sparse sequences ⋮ A density theorem and extreme values of automorphic L-functions at one ⋮ Nonvanishing of the central \(L\)-values with large weight ⋮ Integral mean square estimation for the error term related to \(\sum_{n\leq x}\lambda ^2 (n^2)\) ⋮ A modular analogue of a problem of Vinogradov ⋮ On the fourth moment of coefficients of symmetric square \(L\)-function ⋮ Higher power moments of the Riesz mean error term of symmetric square \(L\)-function ⋮ Unnamed Item ⋮ On the fourth moment of holomorphic Hecke cusp forms ⋮ Special values of symmetric power \(L\)-functions and Hecke eigenvalues ⋮ On central \(L\)-derivative values of automorphic forms ⋮ Asymptotics for the Dirichlet coefficients of symmetric power $L$-functions ⋮ On the first negative Hecke eigenvalue of an automorphic representation of \(\mathrm{GL}_2(\mathbb{A}_\mathbb{Q})\) ⋮ Some notes on distribution of Hecke eigenvalues for Maass cusp forms ⋮ Ternary quadratic form with prime variables attached to Fourier coefficients of primitive holomorphic cusp form ⋮ On the mean-square of the error term related to \(\sum_{n\leq x} \lambda^2 (n^j)\) ⋮ Mean square estimates for coefficients of symmetric power \(L\)-functions ⋮ Distribution of Maass of holomorphic cusp forms ⋮ Unnamed Item ⋮ A sieve method for shifted convolution sums ⋮ Distribution of values at 1 of symmetric power $L$-functions of Maass cusp forms ⋮ Some remarks on the coefficients of symmetric power 𝐿-functions
Cites Work
- Quelques applications du théorème de densité de Chebotarev
- Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman
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- Moyennes de certaines fonctions multiplicatives sur les entiers friables
- Interprétation combinatoire des moments négatifs des valeurs de fonctions L au bord de la bande critique
- Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
- Répartition asymptotique des valeurs propres de l’opérateur de Hecke 𝑇_𝑝
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