On Multiple Polylogarithms in Characteristic $p$: $v$-Adic Vanishing Versus $\infty$-Adic Eulerianness

DOI10.1093/IMRN/RNX151zbMath1479.11158arXiv1511.03490OpenAlexW2964102358MaRDI QIDQ5243310

Yoshinori Mishiba, Chieh-Yu Chang

Publication date: 18 November 2019

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.03490

zbMATH Keywords

\(t\)-modulesCarlitz multiple polylogarithms\(\infty\)-adic Eulerian\(v\)-adic vanishing

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Transcendence theory of Drinfel'd and (t)-modules (11J93) Special functions in characteristic (p) (gamma functions, etc.) (33E50) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20) Zeta and (L)-functions in characteristic (p) (11M38) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items (10)

Taylor coefficients of Anderson-Thakur series and explicit formulae ⋮ On ∞-adic and v-adic multiple zeta functions in positive characteristic ⋮ Integrality of \(v \)-adic multiple zeta values ⋮ Multiple zeta functions and polylogarithms over global function fields ⋮ Deformation of multiple zeta values and their logarithmic interpretation in positive characteristic ⋮ On a conjecture of Furusho over function fields ⋮ Special values of Goss \(L\)-series attached to Drinfeld modules of rank 2 ⋮ On multi-poly-Bernoulli-Carlitz numbers ⋮ Analytic continuation of multiple polylogarithms in positive characteristic ⋮ Factorization of coefficients for exponential and logarithm in function fields

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