Functional identities for L-series values in positive characteristic

Abstract

Abstract. In this paper we show the existence of functional relations for a class of L-series introduced by the second author in [13]. Our results will be applied to obtain a new class of congruences for BernoulliCarlitz fractions, and an analytic conjecture is stated, implying an interesting behavior of such fractions modulo prime ideals of Fq [θ].

Special zeta values using tensor powers of Drinfeld modules

“…Remark 6.1. We remark that Pellarin, Angles, Ribeiro and Perkins develope a multivariable version of L-series in [8]- [11], [36], [37] and that it is possible that such considerations could enable one to obtain formulas for all zeta values; this is an area of ongoing study.…”

Taelman L-values for Drinfeld modules over Tate algebras

“…Remark 5.6. We note that Lemma 5.5 can be seen as a corollary of Simon's Lemma [2,Lem. 4] when φ = C. Lemma 5.7.…”

“…Theorem 1.1. Let φ be a Drinfeld A-module defined as in (1) and ϕ be a Drinfeld A-module defined as in (2). Let L(ϕ, A) be the Taelman L-value corresponding to ϕ. Then…”

“…Corollary 1.3. Let φ be a Drinfeld A-module defined as in (1), and ϕ be a Drinfeld A-module defined as in (2). If 0 ≤ n ≤ q/r − (1 + 2β), then…”

“…. , z n ; x, y) is entire on C ∞ × S ∞ , and Anglès and Pellarin [2,Prop. 6] proved the same result for arbitrary n.…”