Special \(L\)-values and shtuka functions for Drinfeld modules on elliptic curves

DOI10.1007/s40687-018-0122-8zbMath1441.11150arXiv1607.04211OpenAlexW2962978535WikidataQ60118076 ScholiaQ60118076MaRDI QIDQ2319733

Nathan Green, Matthew A. Papanikolas

Publication date: 20 August 2019

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.04211

zbMATH Keywords

Drinfeld modulesAnderson generating functionsreciprocal sumslog-algebraicityPellarin \(L\)-seriesshtuka functions

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Drinfel'd modules; higher-dimensional motives, etc. (11G09) Zeta and (L)-functions in characteristic (p) (11M38) Difference algebra (12H10)

Related Items (14)

Special functions and Gauss-Thakur sums in higher rank and dimension ⋮ Taylor coefficients of Anderson-Thakur series and explicit formulae ⋮ Effective rigid analytic trivializations for Drinfeld modules ⋮ Algebraic relations among Goss’s zeta values on elliptic curves ⋮ Residue of special functions of Anderson \(A\)-modules at the characteristic graph ⋮ Universal families of Eulerian multiple zeta values in positive characteristic ⋮ Special functions and twisted L-series ⋮ Zeta-like multizeta values for higher genus curves ⋮ Recent developments in the theory of Anderson modules ⋮ Product formulas for periods of CM abelian varieties and the function field analog ⋮ Tensor powers of rank 1 Drinfeld modules and periods ⋮ Hyperderivative power sums, Vandermonde matrices, and Carlitz multiplication coefficients ⋮ On identities for zeta values in Tate algebras ⋮ Factorization of coefficients for exponential and logarithm in function fields

Cites Work

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• On certain generating functions in positive characteristic
• Twisted characteristic \(p\) zeta functions
• Functional identities for \(L\)-series values in positive characteristic
• Explicit formulae for \(L\)-values in positive characteristic
• Tensor powers of the Carlitz module and zeta values
• Special \(L\)-values of Drinfeld modules
• Gamma functions for function fields and Drinfeld modules
• On a new type of \(L\)-function for algebraic curves over finite fields
• \(t\)-motives
• Rank one elliptic \(A\)-modules and \(A\)-harmonic series
• Periods of \(t\)-motives and transcendence
• Rigid analytic geometry and its applications
• Determination of the algebraic relations among special \(\Gamma\)-values in positive characteristic
• Shtukas and Jacobi sums
• Log-algebraicity of twisted \(A\)-harmonic series and special values of \(L\)-series in characteristic \(p\)
• Values of certain \(L\)-series in positive characteristic
• On the \(L\)-series of F. Pellarin
• Algebraic independence of values of Goss \(L\)-functions at \(s=1\)
• Pink's theory of Hodge structures and the Hodge conjecture over function fields
• Universal Gauss-Thakur sums and \(L\)-series
• Identities for Anderson generating functions for Drinfeld modules
• Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms
• On certain functions connected with polynomials in a Galois field
• Arithmetic of positive characteristic -series values in Tate algebras
• Algebraic relations among periods and logarithms of rank 2 Drinfeld modules
• Algebraic independence of periods and logarithms of Drinfeld modules
• On Pellarin’s $L$-series
• The Arithmetic of Elliptic Curves
• Rank-One Drinfeld Modules on Elliptic Curves
• Linear independence of Gamma values in positive characteristic
• Anderson-Stark units for 𝔽_{𝕢}[𝜃]
• Stark units in positive characteristic
• Special functions and twisted L-series

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