Some aspects and applications of the Riemann hypothesis over finite fields

DOI10.1007/s00032-010-0111-xzbMath1271.11113OpenAlexW2045364973MaRDI QIDQ627060

Emmanuel Kowalski

Publication date: 19 February 2011

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://doc.rero.ch/record/314428/files/32_2010_Article_111.pdf

zbMATH Keywords

Deligne equidistribution theoremExponential sums over finite fields

Mathematics Subject Classification ID

Exponential sums (11T23) Étale and other Grothendieck topologies and (co)homologies (14F20) Finite ground fields in algebraic geometry (14G15) Gauss and Kloosterman sums; generalizations (11L05)

Related Items

Gauss sums over some matrix groups, Ax's theorem with an additive character, On the motivic oscillation index and bound of exponential sums modulo \(p^m\) via analytic isomorphisms, On the size of 𝑝-adic Whittaker functions

Cites Work

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• On Kahane's ultraflat polynomials
• La conjecture de Weil. II
• Effective counting of the points of definable sets over finite fields
• The cubic moment of central values of automorphic \(L\)-functions
• La conjecture de Weil. I
• Big symplectic or orthogonal monodromy modulo \(\ell\)
• Twisted L-Functions and Monodromy. (AM-150)
• Mod-Poisson Convergence in Probability and Number Theory
• Exponential sums over finite fields and differential equations over the complex numbers: Some interactions
• Finding meaning in error terms
• Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116)
• Mordell’s exponential sum estimate revisited
• ON THE RANK OF QUADRATIC TWISTS OF ELLIPTIC CURVES OVER FUNCTION FIELDS
• Moments, Monodromy, and Perversity. (AM-159)
• Numbers of solutions of equations in finite fields
• Sums of Betti numbers in arbitrary characteristic.