$p$-adic estimates for exponential sums and the theorem of Chevalley-Warning

DOI10.24033/asens.1543zbMath0654.12011OpenAlexW194821603WikidataQ105627631 ScholiaQ105627631MaRDI QIDQ3800162

Alan Adolphson, Steven I. Sperber

Publication date: 1987

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1987_4_20_4_545_0

zbMATH Keywords

L-functionsp-divisibility of certain exponential sums over finite fieldstheorem of Chevalley-Warning

Mathematics Subject Classification ID

Exponential sums (11T23) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Estimates on character sums (11L40)

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Cites Work

• Unnamed Item
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• Unnamed Item
• Completely continuous endomorphisms of \(p\)-adic Banach spaces
• Séries de Dirichlet et intégrales associées à un polynôme à deux indéterminées. (Dirichlet series and integrals associated with a polynomial of two variables)
• Newton polyhedra and the degree of the L-function associated to an exponential sum
• Minimal characteristic exponent of the Gauss-Manin connexion of an isolated singular point and Newton polyhedron
• Polyedres de Newton et nombres de Milnor
• Bemerkung zur vorstehenden Arbeit von Herrn Chevalley
• On the zeta function of a hypersurface. I
• Frobenius and the Hodge filtration (estimates)
• On the p-adic Theory of Exponential Sums
• Exponential Sums on the Complement of a Hypersurface
• On a Theorem of Ax
• Zeroes of Polynomials Over Finite Fields
• Numbers of solutions of equations in finite fields

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