Geodesic
Vanishing of multizeta values over $\mathbb {F}_q[t]$ at negative integers
Canadian mathematical bulletin, Tome 65 (2022) no. 1, pp. 9-29

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DOI

Let $\mathbb {F}_q$ be the finite field of q elements. In this paper, we study the vanishing behavior of multizeta values over $\mathbb {F}_q[t]$ at negative integers. These values are analogs of the classical multizeta values. At negative integers, they are series of products of power sums $S_d(k)$ which are polynomials in t. By studying the t-valuation of $S_d(s)$ for $s < 0$, we show that multizeta values at negative integers vanish only at trivial zeros. The proof is inspired by the idea of Sheats in the proof of a statement of “greedy element” by Carlitz.
DOI : 10.4153/S0008439521000035
Mots-clés : multizeta values, vanishing at negative integers, trivial zero, power sum, valuation monotonicity, modest element 
Shi, Shuhui. Vanishing of multizeta values over $\mathbb {F}_q[t]$ at negative integers. Canadian mathematical bulletin, Tome 65 (2022) no. 1, pp. 9-29. doi: 10.4153/S0008439521000035
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     title = {Vanishing of multizeta values over $\mathbb {F}_q[t]$ at negative integers},
     journal = {Canadian mathematical bulletin},
     pages = {9--29},
     year = {2022},
     volume = {65},
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