Another look at Zagier's formula for multiple zeta values involving Hoffman elements

2020/11/23 by Cezar Lupu, Lupu, Cezar · 2 citations
Chemistry · Materials Science · Mathematics · #11B65 #11B68 #11M06 #11M32 #Advanced Mathematical Identities #Crystallization and Solubility Studies #FOS: Mathematics #Molecular spectroscopy and chirality #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2011.11718

openalex publication_date 2020/11/23 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In this paper, we give an elementary account into Zagier's formula for multiple zeta values involving Hoffman elements. Our approach allows us to obtain direct proof in a special case via rational zeta series involving the coefficient ζ(2n). This formula plays an important role in proving Hoffman's conjecture which asserts that every multiple zeta value of weight k can be expressed as a ℚ-linear combinations of multiple zeta values of the same weight involving 2's and 3's. Also, using a similar hypergeometric argument via rational zeta series, we produce a new Zagier-type formula for the multiple special Hurwitz zeta values.

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