Integral mean-square estimation of error terms of Fourier coefficients attached to cusp forms

DOI10.1007/s12044-023-00737-3zbMath1523.11069OpenAlexW4379988271MaRDI QIDQ6175461

Guodong Hua

Publication date: 24 July 2023

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12044-023-00737-3

zbMATH Keywords

automorphic \(L\)-functionsLanglands programHecke eigenforms

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Holomorphic modular forms of integral weight (11F11)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Level raising and symmetric power functoriality. II
• Level-raising and symmetric power functoriality. III.
• A family of Calabi-Yau varieties and potential automorphy. II.
• On the mean-square of the error term related to \(\sum_{n\leq x} \lambda^2 (n^j)\)
• On the Rankin-Selberg problem
• Integral mean square estimation for the error term related to \(\sum_{n\leq x}\lambda ^2 (n^2)\)
• Perron's formula and the prime number theorem for automorphic \(L\)-functions
• Local coefficients as Artin factors for real groups
• General L-functions
• Fourier coefficients of cusp forms and automorphic \(L\)-functions
• A proof of Langlands' conjecture on Plancherel measures; complementary series for \(p\)-adic groups
• La conjecture de Weil. I
• 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
• Symmetric power functoriality for holomorphic modular forms
• Symmetric power functoriality for holomorphic modular forms. II.
• Sign changes and nonvanishing of Fourier coefficients of holomorphic cusp forms
• Decoupling, exponential sums and the Riemann zeta function
• Level-raising and symmetric power functoriality, I
• Rankin-Selberg Convolutions
• SUMS OF FOURIER COEFFICIENTS OF CUSP FORMS
• Power sums of Hecke eigenvalues and application
• Fourier Transforms of Intertwining Operators and Plancherel Measures for GL(n)
• On Certain L-Functions
• On Euler Products and the Classification of Automorphic Representations I
• On Euler Products and the Classification of Automorphic Forms II
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• On Riesz means of the coefficients of the Rankin–Selberg series
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• A new subconvex bound for GL(3) L-functions in the t-aspect
• Asymptotics for the Dirichlet coefficients of symmetric power $L$-functions

This page was built for publication: Integral mean-square estimation of error terms of Fourier coefficients attached to cusp forms