Explicit upper bounds for 𝐿-functions on the critical line

DOI10.1090/S0002-9939-09-10075-8zbMath1243.11088arXiv0906.4177MaRDI QIDQ3648165

Vorrapan Chandee

Publication date: 24 November 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.4177

zbMATH Keywords

\(L\)-functionsgeneralized Riemann hypothesisLindelöf hypothesisestimates on critical line

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Other Dirichlet series and zeta functions (11M41) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Real zeros of (L(s, chi)); results on (L(1, chi)) (11M20) Zeta functions and (L)-functions of number fields (11R42) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (22)

Quantum variance for dihedral Maass forms ⋮ Moments of the products of quadratic twists of automorphic \(L\)-functions ⋮ Higher integral moments of automorphic \(L\)-functions in short intervals ⋮ Explicit bound for the number of primes in arithmetic progressions assuming the Generalized Riemann Hypothesis ⋮ Representation by ternary quadratic forms ⋮ Simple zeros of modular L -functions ⋮ Signs of Fourier coefficients of half-integral weight modular forms ⋮ ON FUNDAMENTAL FOURIER COEFFICIENTS OF SIEGEL CUSP FORMS OF DEGREE 2 ⋮ Estimates for \(L\)-functions in the critical strip under GRH with effective applications ⋮ Bounding \(\zeta(s)\) in the critical strip ⋮ Mollified moments of cubic Dirichlet \(L\)-functions over the Eisenstein field ⋮ Moments of automorphic \(L\)-functions in the strip \(\frac{1}{2}<\sigma <1\) ⋮ Conditional estimates for the logarithmic derivative of Dirichlet \(L\)-functions ⋮ The distribution of values of zeta and \(L\)-functions ⋮ SHIFTED MOMENTS OF ‐FUNCTIONS AND MOMENTS OF THETA FUNCTIONS ⋮ Explicit bounds for \(L\)-functions on the edge of the critical strip ⋮ A sum of three nonzero triangular numbers ⋮ Upper bounds for the moments of derivatives of Dirichlet \(L\)-functions ⋮ Moments of products of automorphic \(L\)-functions ⋮ Quantum unique ergodicity for half-integral weight automorphic forms ⋮ A generalization of a method of Mordell to ternary quadratic forms ⋮ Conditional bounds for the least quadratic non-residue and related problems

Cites Work

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• Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids
• Moments of the Riemann zeta function
• Ramanujan's ternary quadratic form
• On modular forms of half integral weight
• The analytic theory of algebraic numbers
• Kaplansky's ternary quadratic form

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