Tensor Powers of the Carlitz Module and Zeta Values

Abstract

K, =: an algebraic closure of K ,. K X p=: the separable algebraic closure of K in K,. G , =: the additive group over A. *Sloan fellow, also supported by NSF grant DMS-8610730(2) **Supportedby NSF grant DMS-8610730C2 , Transcendence and special zeta values in characteristic p, preprint, 1988. Added in proof. Jing Yu has also proved the transcendence of the v-adic zeta values for n not divisible by q-1.

Functional identities for L-series values in positive characteristic

“…apparent in (2), this implies that, for m ≥ 0 integer, V q m ,1 (t) := π where BC n and Π(n) denote respectively the n-th Bernoulli-Carlitz fraction and Carlitz's factorial of n, see Goss' book [11, Section 9.1]. Indeed, evaluating at t = θ, we get…”

Values of certain L-series in positive characteristic

“…Following the terminology of the authors, it is a rigid analytic trivialization of Carlitz's t-motive. The functions ω, Ω also appear, under several different notations, in the papers [1], [5], [4], [31]. In [1], the function ω is related to the theory of scattering matrices (see Section 3.1 of loc.…”

Transcendence of Periods: The State of the Art

“…This element of C is transcendental over F q (T ): this was proved by G.W. Anderson and D. Thakur in 1990 [4]. An interesting remark of them is that the tools which were available to I.I.…”