Statistics for low-lying zeros of symmetric power L-functions in the level aspect

DOI10.1515/FORM.2011.035zbMath1264.11080arXivmath/0703760OpenAlexW2953158153MaRDI QIDQ3093166

Emmanuel Royer, Guillaume Ricotta

Publication date: 12 October 2011

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703760

zbMATH Keywords

random matrix theoryzeros of L-functionsKatz-Sarnak conjecturessymmetry types

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Holomorphic modular forms of integral weight (11F11) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41) Relations with random matrices (11M50)

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Cites Work

• Low-lying zeros of \(L\)-functions with orthogonal symmetry
• Kloosterman sums and Fourier coefficients of cusp forms
• The highest lowest zero and other applications of positivity
• Cuspidality of symmetric powers with applications.
• Rankin-Selberg \(L\)-functions in the level aspect.
• Functorial products for \(\text{GL}_2\times \text{GL}_3\) and the symmetric cube for \(\text{GL}_2\).
• The central limit theorem for local linear statistics in classical compact groups and related combinatorial identities
• Hecke operators on \(\Gamma_0(m)\)
• Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung. I
• Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung. II
• A Burgess-like subconvex bound for twisted L-functions
• On the Conjecture of Birch and Swinnerton-Dyer for an Elliptic Curve of Rank 3
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• One- and two-level densities for rational families of elliptic curves: evidence for the underlying group symmetries
• On Kloosterman's sum
• Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung