Algebraic relations among Goss’s zeta values on elliptic curves

DOI10.1017/fms.2023.94arXiv2004.08461MaRDI QIDQ6052074

Nathan Green, Ngo Dac Tuan

Publication date: 23 October 2023

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.08461

Mathematics Subject Classification ID

Drinfel'd modules; higher-dimensional motives, etc. (11G09) Transcendence theory of Drinfel'd and (t)-modules (11J93) Zeta and (L)-functions in characteristic (p) (11M38)

Cites Work

• Special \(L\)-values of abelian \(t\)-modules
• Arithmetic of function field units
• Frobenius difference equations and algebraic independence of zeta values in positive equal characteristic
• Tensor powers of the Carlitz module and zeta values
• Special \(L\)-values of Drinfeld modules
• On special \(L\)-values of \(t\)-modules
• Transcendence and special zeta values in characteristic p
• Algebraic independence of arithmetic gamma values and Carlitz zeta values
• On a new type of \(L\)-function for algebraic curves over finite fields
• \(t\)-motives
• An addendum to ``\(v\)-adic zeta functions, \(L\)-series, and measures for function fields
• Rank one elliptic \(A\)-modules and \(A\)-harmonic series
• Analytic homomorphisms into Drinfeld modules
• 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
• Algebraic independence of values of Goss \(L\)-functions at \(s=1\)
• Recent developments in the theory of Anderson modules
• Special zeta values using tensor powers of Drinfeld modules
• Tensor powers of rank 1 Drinfeld modules and periods
• A class formula for admissible Anderson modules
• On Zagier-Hoffman's conjectures in positive characteristic
• A rapid introduction to Drinfeld modules, \(t\)-modules, and \(t\)-motives
• Pink's theory of Hodge structures and the Hodge conjecture over function fields
• Frobenius difference equations and difference Galois groups
• Multizeta in function field arithmetic
• Special \(L\)-values and shtuka functions for Drinfeld modules on elliptic curves
• Determination of algebraic relations among special zeta values in positive characteristic
• Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms
• On certain functions connected with polynomials in a Galois field
• A class formula for \(L\)-series in positive characteristic
• 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
• Geometric Gamma Values and Zeta Values in Positive Characteristic
• The Arithmetic of Elliptic Curves
• ELLIPTIC MODULES
• Anderson-Stark units for 𝔽_{𝕢}[𝜃]
• Transcendental numbers and special values of Dirichlet series
• Exceptional Zeros of L-series and Bernoulli- Carlitz Numbers
• Stark units in positive characteristic
• Special functions and twisted L-series
• Multizeta values for function fields: A survey
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