Exponential sums with multiplicative coefficients without the Ramanujan conjecture

DOI10.1007/s00208-020-02108-zzbMath1464.11083OpenAlexW3108795105WikidataQ115609077 ScholiaQ115609077MaRDI QIDQ2225624

Guangshi Lü, Yujiao Jiang, Zhiwei Wang

Publication date: 8 February 2021

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-020-02108-z

zbMATH Keywords

exponential sumsautomorphic \(L\)-functions

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Fourier coefficients of automorphic forms (11F30) Applications of sieve methods (11N36)

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Cites Work

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• Shifted convolution sums for \(\mathrm{GL}(3)\times\mathrm{GL}(2)\)
• A family of Calabi-Yau varieties and potential automorphy. II.
• Weak subconvexity for central values of \(L\)-functions
• Sieving for mass equidistribution
• Hyperbolic prime number theorem
• Automorphic distributions, \(L\)-functions, and Voronoi summation for \(\text{GL}(3)\)
• A sieve method for shifted convolution sums
• On the absolute value of Ramanujan's \(\tau\)-function
• An upper bound on conductors for pairs
• An additive problem in the Fourier coefficients of cusp forms
• La conjecture de Weil. I
• Upper and lower bounds at \(s=1\) for certain Dirichlet series with Euler product.
• Absolute convergence of the spectral side of the Arthur trace formula for \(\text{GL}_n\)
• On Selberg's eigenvalue conjecture
• Zeros of principal \(L\)-functions and random matrix theory
• Weak subconvexity without a Ramanujan hypothesis
• Linnik-type problems for automorphic \(L\)-functions
• Standard zero-free regions for Rankin-Selberg \(L\)-functions via sieve theory
• The circle method and bounds for \(L\)-functions. I
• Effective multiplicity one on GL n and narrow zero-free regions for Rankin-Selberg L- functions
• On Certain L-Functions
• Entiers Sans Grand Facteur Premier En Progressions Arithmetiques
• On exponential sums with multiplicative coefficients, II
• Sur L'Equirepartition Modulo 1 De Certaines Fonctions De Diviseurs
• Disjointness of Moebius from Horocycle Flows
• AN EXTENSION OF THE BOURGAIN–SARNAK–ZIEGLER THEOREM WITH MODULAR APPLICATIONS
• Upper Bounds on L-Functions at the Edge of the Critical Strip
• Cancellation in additively twisted sums on GL(n)
• Das asymptotische Verhalten von Summen über multiplikative Funktionen. II
• ON A CERTAIN GENERAL EXPONENTIAL SUM
• Exponential sums with multiplicative coefficients