Values of certain L-series in positive characteristic

Abstract

We introduce a family of L-series specialising to both L-series associated to certain Dirichlet characters over F_q[T] and to integral values of Carlitz-Goss zeta function associated to F_q[T]. We prove, with the use of the theory of deformations of vectorial modular forms, a formula for their value at 1, as well as some arithmetic properties of other values at positive integers

Cited by in corpus (13)

• Arithmetic of positive characteristic L-series values in Tate algebras
• Arithmetic of characteristic p special L-values (with an appendix by V. Bosser)
• Explicit Formulae for $L$-values in Positive Characteristic
• The de Rham isomorphism for Drinfeld modules over Tate algebras
• Hyperderivatives of periods and quasi-periods for Anderson $t$-modules
• An exact degree for multivariate special polynomials
• On the generalized Carlitz module
• Effective rigid analytic trivializations for Drinfeld modules
• Special Functions and Gauss-Thakur Sums in Higher Rank and Dimension
• Hyperderivative power sums, Vandermonde matrices, and Carlitz multiplication coefficients
• An Integral Digit Derivative Basis for Carlitz Prime Power Torsion Extensions
• A duality result about special functions in Drinfeld modules of arbitrary rank
• Residue of special functions of Anderson $A$-modules at the characteristic graph