\(L\)-functions associated with families of toric exponential sums

DOI10.1016/j.jnt.2014.03.016zbMath1296.11162arXiv1109.3682OpenAlexW2013012036MaRDI QIDQ404363

C. Douglas Haessig, Steven I. Sperber

Publication date: 4 September 2014

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.3682

zbMATH Keywords

exponential sums\(L\)-functions\(p\)-adic cohomologyDwork theory

Mathematics Subject Classification ID

Exponential sums (11T23) Zeta functions and (L)-functions (11S40)

Related Items

Newton polygons for \(L\)-functions of generalized Kloosterman sums ⋮ \(L\)-functions of symmetric powers of Kloosterman sums (unit root \(L\)-functions and \(p\)-adic estimates) ⋮ Unit roots of the unit root \(L\)-functions of Kloosterman family ⋮ Kloosterman sums and Hecke polynomials in characteristics 2 and 3 ⋮ \(p\)-adic variation of unit root \(L\)-functions ⋮ Symmetric power $L$-functions for families of generalized Kloosterman sums

Cites Work

• Unnamed Item
• Unnamed Item
• Exponential sums and Newton polyhedra: cohomology and estimates
• Newton polyhedra and the degree of the L-function associated to an exponential sum
• The \(U_p\)-operator of Atkin on modular functions of level three
• La conjecture de Weil. II
• Weights of exponential sums, intersection cohomology, and Newton polyhedra
• Bessel functions as p-adic functions of the argument
• A p-adic theory of Hecke polynomials
• On exponential sums in finite fields. II
• Exponential sums on \((\mathbb{G}_ m)^ n\)
• Meromorphic continuation of \(L\)-functions of \(p\)-adic representations
• Dwork's conjecture on unit root zeta functions
• On the zeta function of a hypersurface. II
• Trivial factors for \(L\)-functions of symmetric products of Kloosterman sheaves
• Hecke polynomials as congruence \(\zeta\) functions in elliptic modular case
• On Hecke polynomials
• Normalized period matrices. II
• L-FUNCTIONS OF SYMMETRIC POWERS OF THE GENERALIZED AIRY FAMILY OF EXPONENTIAL SUMS
• Computing the Continuous Discretely
• L-functions of symmetric powers of cubic exponential sums
• Symmetric powers of the p-adic Bessel equation.
• $p$-adic estimates for exponential sums and the theorem of Chevalley-Warning
• Higher rank case of Dwork’s conjecture
• Rank one case of Dwork’s conjecture
• A semicontinuity result for monodromy under degeneration
• On Exponential Sums in Finite Fields
• On the Rationality of the Zeta Function of an Algebraic Variety
• On a Theorem of Ax
• Moments, Monodromy, and Perversity. (AM-159)
• L-functions for symmetric products of Kloosterman sums
• Zeroes of Polynomials Over Finite Fields