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Article Dans Une Revue Hardy-Ramanujan Journal Année : 2024

Identities among some combinatorial objects involving special values of multiple zeta functions

Résumé

In the article, we establish some identities involving special values of multiple zeta functions among the counting functions of number of representations of an integer by a linear combination of figurate numbers such as triangular numbers, square numbers, pentagonal numbers, etc. More precisely, we provide our result for $\delta_k(n)$, $r_{k}(n)$ and $\mathcal{N}_{k}^{a}(n)$ (for a fixed $a \ge 3$), the number of representations of $n$ as a sum of $k$-triangular numbers, as a sum of $k$-square numbers and as a sum of $k$-higher figurate numbers (for a fixed $a \ge 3$), respectively. Moreover, these identities also occur when one of $\delta_k(n)$, $r_{k}(n)$ and $\mathcal{N}_{k}^{a}(n)$ is replaced by the $k$-colored partition functions.
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Dates et versions

hal-04443007 , version 1 (07-02-2024)
hal-04443007 , version 2 (11-02-2024)

Licence

Paternité - Pas d'utilisation commerciale

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Lalit Vaishya. Identities among some combinatorial objects involving special values of multiple zeta functions. Hardy-Ramanujan Journal, 2024, 46, pp.42 -- 50. ⟨10.46298/hrj.2024.13032⟩. ⟨hal-04443007v2⟩
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