staple
With cedram.org

Search the site

Table of contents for this issue | Previous article | Next article
Federico Pellarin
A sum-shuffle formula for zeta values in Tate algebras
Journal de théorie des nombres de Bordeaux, 29 no. 3 (2017), p. 1025-1048, doi: 10.5802/jtnb.1010
Article PDF
Class. Math.: 11M38
Keywords: Multiple zeta values, Function field arithmetic, Carlitz zeta values

Résumé - Abstract

We prove a sum-shuffle formula for multiple zeta values in Tate algebras (in positive characteristic), introduced in [9]. This follows from an analog result for double twisted power sums, implying that an $\mathbb{F}_p$-vector space generated by multiple zeta values in Tate algebras is an $\mathbb{F}_p$-algebra.

Bibliography

[1] Bruno Anglès, Tuan Ngo Dac & Floric Tavares Ribeiro, “Exceptional zeros of $L$-series and Bernoulli-Carlitz numbers”, https://arxiv.org/abs/1511.06209v2, 2015
[2] Bruno Anglès & Federico Pellarin, Functional identities for $L$-series values in positive characteristic, J. Number Theory 142 (2014), p. 223-251 Article
[3] Bruno Anglès & Federico Pellarin, Universal Gauss-Thakur sums and $L$-series, Invent. Math. 200 (2015), p. 653-669 Article
[4] Bruno Anglès, Federico Pellarin & Floric Tavares Ribeiro, Arithmetic of positive characteristic $L$-series values in Tate algebras, Compos. Math. 152 (2016), p. 1-61 Article
[5] Chieh-Yu Chang & Jing Yu, Determination of algebraic relations among special zeta values in positive characteristic, Adv. Math. 216 (2007), p. 321-345 Article
[6] Huei-Jeng Chen, On shuffle of double zeta values over $\mathbb{F}_q[t]$, J. Number Theory 148 (2015), p. 153-163 Article
[7] F. Demeslay, Formule de classes en caractéristique positive, Ph. D. Thesis, Université de Normandie (France), 2015
[8] Federico Pellarin, Values of certain $L$-series in positive characteristic, Ann. Math. 176 (2012), p. 2055-2093 Article
[9] Federico Pellarin, A note on multiple zeta values in Tate algebras, Riv. Mat. Univ. Parma 7 (71–100)
[10] Federico Pellarin & Rudolph Perkins, “On twisted $A$-harmonic sums and Carlitz finite zeta values”, https://arxiv.org/abs/1512.05953, 2016
[11] Lenny Taelman, Special $L$-values of Drinfeld modules, Ann. Math. 175 (2012), p. 369-391 Article
[12] Dinesh S. Thakur, Shuffle Relations for Function Field Multizeta Values, Int. Math. Res. Not. 2010 (2010), p. 1973-1980
[13] Dinesh S. Thakur, Power sums of polynomials over finite fields and applications: a survey, Finite Fields Appl. 32 (2015), p. 171-191 Article