Integrable systems and number theory in finite characteristic

DOI10.1016/S0167-2789(01)00153-1zbMath0993.11029OpenAlexW2137671661MaRDI QIDQ5940193

Dinesh S. Thakur

Publication date: 21 September 2002

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(01)00153-1

zbMATH Keywords

gammasolitonDrinfeld modulesShtukathetazeta

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Drinfel'd modules; higher-dimensional motives, etc. (11G09)

Related Items (5)

The algebraic dynamics of the pentagram map ⋮ Arithmetic of Gamma, Zeta and Multizeta Values for Function Fields ⋮ Power sums of polynomials over finite fields and applications: a survey ⋮ Hypergeometric functions for function fields and transcendence ⋮ Transcendence in positive characteristic and special values of hypergeometric functions

Cites Work

• Deligne's reciprocity for function fields
• Tensor powers of the Carlitz module and zeta values
• Gamma functions for function fields and Drinfeld modules
• Loop groups and equations of KdV type
• \(t\)-motives
• An alternate approach to solitons for \(\mathbb F_q [t\)]
• Rank one elliptic \(A\)-modules and \(A\)-harmonic series
• Torsion points on Jacobians of quotients of Fermat curves and \(p\)-adic soliton theory
• Analytic homomorphisms into Drinfeld modules
• Periods of \(t\)-motives and transcendence
• Shtukas and Jacobi sums
• Hecke characters and Eisenstein reciprocity in function fields
• Log-algebraicity of twisted \(A\)-harmonic series and special values of \(L\)-series in characteristic \(p\)
• Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–
• ELLIPTIC MODULES
• Linear independence of Gamma values in positive characteristic
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