Weak subconvexity without a Ramanujan hypothesis

DOI10.1215/00127094-2018-0065zbMath1426.11053arXiv1804.03654OpenAlexW3099364428MaRDI QIDQ2001643

Jesse Thorner, Kannan Soundararajan

Publication date: 10 July 2019

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.03654

zbMATH Keywords

subconvexityautomorphic \(L\)-functionSelberg classaxiomzero-density estimatelog-free

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Turán theory (11N30)

Related Items (12)

Cancellation in algebraic twisted sums on \(\operatorname{GL}_m\) ⋮ Towards a 𝐺𝐿_{𝑛} variant of the Hoheisel phenomenon ⋮ Zeros of Rankin-Selberg \(L\)-functions at the edge of the critical strip ⋮ Möbius randomness law for 𝐺𝐿(𝑚) automorphic 𝐿-functions twisted by additive characters ⋮ Exponential sums with coefficients of the logarithmic derivative of automorphic \(L\)-functions and applications ⋮ Zeros of Rankin–Selberg L-functions in families ⋮ An approximate form of Artin's holomorphy conjecture and non-vanishing of Artin \(L\)-functions ⋮ An unconditional \(\mathrm{GL}_n\) large sieve ⋮ Exponential sums with multiplicative coefficients without the Ramanujan conjecture ⋮ Effective forms of the Sato-Tate conjecture ⋮ Patterns of primes in the Sato-Tate conjecture ⋮ Large values of Dirichlet L-functions at zeros of a class of L-functions

Cites Work

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• Weak subconvexity for central values of \(L\)-functions
• On the Ramanujan conjecture over number fields
• Large character sums: Burgess's theorem and zeros of \(L\)-functions
• An upper bound on conductors for pairs
• Modularity of the Rankin-Selberg \(L\)-series, and multiplicity one for \(\mathrm{SL}(2)\)
• Functorial products for \(\text{GL}_2\times \text{GL}_3\) and the symmetric cube for \(\text{GL}_2\).
• Zeros of families of automorphic \(L\)-functions close to 1.
• Absolute convergence of the spectral side of the Arthur trace formula for \(\text{GL}_n\)
• Zeros of principal \(L\)-functions and random matrix theory
• Standard zero-free regions for Rankin-Selberg \(L\)-functions via sieve theory
• A large sieve density estimate near \(\sigma = 1\)
• Zeta functions of simple algebras
• Rankin-Selberg Convolutions
• On some new theorems in the theory of diophantine approximations
• Effective multiplicity one on GL n and narrow zero-free regions for Rankin-Selberg L- functions
• Le spectre résiduel de ${\rm GL}(n)$
• Convexity bounds for L-functions
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• Strong exponent bounds for the local Rankin-Selberg convolution
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• Nonvanishing of L-functions, the Ramanujan Conjecture, and Families of Hecke Characters
• Upper Bounds on L-Functions at the Edge of the Critical Strip
• Effective Log-Free Zero Density Estimates for Automorphic L-Functions and the Sato–Tate Conjecture
• On sums of Hecke-Maass eigenvalues squared over primes in short intervals
• A Log-Free Zero-Density Estimate and Small Gaps in Coefficients of L-Functions

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