On exponential sums involving Fourier coefficients of cusp forms over primes

DOI10.1016/J.JNT.2016.01.005zbMath1415.11112OpenAlexW2289206936MaRDI QIDQ266629

Fei Hou

Publication date: 13 April 2016

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2016.01.005

zbMATH Keywords

exponential sumscusp formFourier coefficientsymmetric-square

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Sums over primes (11L20)

Related Items (3)

An exponential sum involving Fourier coefficients of eigenforms for \(\mathrm{SL}(2,\mathbb{Z})\) ⋮ Fourier coefficients at primes twisted with exponential functions ⋮ Oscillations of Fourier coefficients of \(\mathrm{GL}(m)\) Hecke-Maass forms and nonlinear exponential functions at primes

Uses Software

• GL(n)pack

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Additive twists of Fourier coefficients of symmetric-square lifts
• Bounds for \(\mathrm{GL}(3) \times \mathrm{GL}(2)\) \(L\)-functions and \(\mathrm{GL}(3)\) \(L\)-functions
• Zero density for automorphic \(L\)-functions
• Oscillations of Hecke eigenvalues at shifted primes
• The prime number theorem for automorphic \(L\)-functions for \(\text{GL}_m\)
• Oscillations of cusp form coefficients over primes
• La conjecture de Weil. I
• On averages of Fourier coefficients of Maass cusp forms
• Oscillations of cusp form coefficients in exponential sums
• Strong orthogonality between the Möbius function, additive characters and Fourier coefficients of cusp forms
• SUMS OF FOURIER COEFFICIENTS OF CUSP FORMS
• On some exponential sums connected with Ramanujan's τ‐function
• Vinogradov's exponential sum over primes
• An elementary method in prime number theory
• The square mean of Dirichlet series associated with cusp forms
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• On stationary phase integrals
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• Automorphic Forms and L-Functions for the GroupGL(n, R)
• Resonance of automorphic forms for 𝐺𝐿(3)
• Low lying zeros of families of \(L\)-functions

This page was built for publication: On exponential sums involving Fourier coefficients of cusp forms over primes