Explicit formulae for \(L\)-values in positive characteristic

DOI10.1007/s00209-014-1315-5zbMath1306.11070arXiv1207.1753OpenAlexW3121224876MaRDI QIDQ463975

Rudolph Bronson Perkins

Publication date: 17 October 2014

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.1753

zbMATH Keywords

finite fieldpositive characteristicBernoulli-Carlitz numbersalgebraic closureAnderson generating functionsAnderson-Thakur functionPellarin's \(L\)-seriesGauss norm

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Zeta and (L)-functions in characteristic (p) (11M38)

Related Items (11)

On certain generating functions in positive characteristic ⋮ Twisted characteristic \(p\) zeta functions ⋮ Vectorial Drinfeld modular forms over Tate algebras ⋮ From the Carlitz exponential to Drinfeld modular forms ⋮ Effective rigid analytic trivializations for Drinfeld modules ⋮ Anderson-Stark units for 𝔽_{𝕢}[𝜃] ⋮ Polynomials of binomial type and Lucas’ Theorem ⋮ Tensor powers of rank 1 Drinfeld modules and periods ⋮ On twisted \(A\)-harmonic sums and Carlitz finite zeta values ⋮ Special \(L\)-values and shtuka functions for Drinfeld modules on elliptic curves ⋮ On symmetric powers of $\tau $-recurrent sequences and deformations of Eisenstein series

Cites Work

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• A Dirichlet unit theorem for Drinfeld modules
• Tensor powers of the Carlitz module and zeta values
• Values of certain \(L\)-series in positive characteristic
• Universal Gauss-Thakur sums and \(L\)-series
• Identities for Anderson generating functions for Drinfeld modules
• On certain functions connected with polynomials in a Galois field
• Arithmetic of positive characteristic -series values in Tate algebras
• On Pellarin’s $L$-series
• Linear operators in local fields of prime characteristic.

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