Analytic $L$-functions: Definitions, theorems, and connections

DOI10.1090/bull/1646zbMath1453.11107arXiv1711.10375OpenAlexW2962748618MaRDI QIDQ4631427

Ralf Schmidt, Ameya Pitale, David W. Farmer, Nathan C. Ryan

Publication date: 29 March 2019

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.10375

zbMATH Keywords

cuspidal automorphic representations\( L\)-functions

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Modular and automorphic functions (11F03) Other Dirichlet series and zeta functions (11M41) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (7)

Varieties via their L-functions ⋮ The second moment of Dirichlet twists of a \(\mathrm{GL}_4\) automorphic \(L\)-function ⋮ On the Northcott property for special values of \(L\)-functions ⋮ Packet structure and paramodular forms ⋮ On the first negative Hecke eigenvalue of an automorphic representation of \(\mathrm{GL}_2(\mathbb{A}_\mathbb{Q})\) ⋮ Riemann-type functional equations. Julia line and counting formulae ⋮ On Selberg's limit theorem for \(L\)-functions over a family of \(\mathrm{GL} (n)\) Hecke-Maass cusp forms

Cites Work

• On the rigid cohomology of certain Shimura varieties
• Galois representations arising from some compact Shimura varieties
• Conducteur des représentations du groupe linéaire
• On the Selberg class of Dirichlet series: Small degrees
• Zeros of principal \(L\)-functions and random matrix theory
• The conjectural connections between automorphic representations and Galois representations
• Transfer of Siegel cusp forms of degree 2
• Weighted Selberg orthogonality and uniqueness of factorization of automorphic L-functions
• Notes on the arithmetic of Hilbert modular forms
• Effective computation of Maass cusp forms
• On Certain L-Functions
• Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120)
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