Metaplectic Ramanujan Conjecture Over Function Fields with Applications to Quadratic Forms

DOI10.1093/imrn/rnt047zbMath1296.11045arXiv1008.0430OpenAlexW3098543028MaRDI QIDQ2878735

S. Ali Altug, Jacob Tsimerman

Publication date: 5 September 2014

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.0430

zbMATH Keywords

function fieldquadratic form\(L\)-functionFourier coefficientshalf-integral weight cusp formsRamanujan conjecture

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Other groups and their modular and automorphic forms (several variables) (11F55) Zeta and (L)-functions in characteristic (p) (11M38) Quadratic forms over local rings and fields (11E08)

Related Items (10)

The second and third moment of \(L(1/2,\chi)\) in the hyperelliptic ensemble ⋮ The mean values of cubic \(L\)-functions over function fields ⋮ Traces, high powers and one level density for families of curves over finite fields ⋮ The Ratios Conjecture and upper bounds for negative moments of 𝐿-functions over function fields ⋮ Selberg's central limit theorem for quadratic Dirichlet \(L\)-functions over function fields ⋮ Moments of quadratic twists of elliptic curve \(L\)-functions over function fields ⋮ Correlation of shifted values of \(L\)-functions in the hyperelliptic ensemble ⋮ On the Waldspurger formula and the metaplectic Ramanujan conjecture over number fields ⋮ On basic and Bass quaternion orders ⋮ Moments of quadratic Dirichlet \(L\)-functions over function fields

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