A conjecture about multiple t-values

2017/12/18 by Biswajyoti Saha, Saha, Biswajyoti
Mathematics · #11M32 #11M35 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1712.06325

openalex publication_date 2017/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For positive integers a₁,…,a_r with a₁ ≥ 2, the multiple t-value t(a₁,…,a_r) is defined by the series ∑_{n1 > … > nr > 0 \atop ni odd} n₁^-a₁ ⋯ n_r^-a_r. For an integer k ≥ 2, the dimension of the \mathbb Q-vector space generated by all the multiple t-values of weight k has been predicted by Hoffman to be the k-th Fibonacci number. In this short note we give a conjectural basis of this vector space.

Citations

• Multiple Lerch zeta functions and an idea of Ramanujan

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