A note on Fourier coefficients of cusp forms on GL n

DOI10.1515/FORUM.2006.007zbMath1108.11041OpenAlexW1973951286MaRDI QIDQ3378371

Henry H. Kim

Publication date: 30 March 2006

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

Full work available at URL: https://doi.org/10.1515/forum.2006.007

zbMATH Keywords

Fourier coefficientscuspidal automorphic representation

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Zeta functions and (L)-functions of number fields (11R42) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (15)

Cancellation of two classes of dirichlet coefficients over Beatty sequences ⋮ Exponential sums formed with the von Mangoldt function and Fourier coefficients of \(\mathrm{GL}(m)\) automorphic forms ⋮ The prime number theorem and hypothesis H with lower-order terms ⋮ Resonance between automorphic forms and exponential functions ⋮ On the Rankin-Selberg \(L\)-function related to the Godement-Jacquet \(L\)-function ⋮ The number of coefficients of automorphic \(L\)-functions for \(\mathrm{GL}_m\) of same signs ⋮ The Bombieri–Vinogradov Theorem on Higher Rank Groups and its Applications ⋮ Correlation of zeros of automorphic \(L\) -functions ⋮ The generalized Bourgain-Sarnak-Ziegler criterion and its application to additively twisted sums on \(\mathrm{GL}_m\) ⋮ Average of Dirichlet coefficients of cuspidal representations related to \(\mathrm{GL}(2)\) ⋮ Oscillations of Fourier coefficients of \(\mathrm{GL}(m)\) Hecke-Maass forms and nonlinear exponential functions at primes ⋮ Hypothesis H and the prime number theorem for automorphic representations ⋮ Zero correlation with lower-order terms for automorphic L-functions ⋮ Moments of products of automorphic \(L\)-functions ⋮ Functoriality of automorphic \(L\)-functions through their zeros

Cites Work

• Sato-Tate conjectures and Chebyshev polynomials
• Cuspidality of symmetric powers with applications.
• Functorial products for \(\text{GL}_2\times \text{GL}_3\) and the symmetric cube for \(\text{GL}_2\).
• Zeros of principal \(L\)-functions and random matrix theory

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