On the Multiple Zeta Values ζ(\2\^k)

2019/11/17 by Mario DeFranco, DeFranco, Mario
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1911.07129

openalex publication_date 2019/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We evaluate the multiple zeta values \ζ( 2 ^k) by proving a certain\nfactorization property. The proof uses a combinatorial bijection and elementary\ntelescoping series. We show how the infinite product for the sine function in\nfact implies its power series and other trigonometric properties. We define two\nconstants, which we call pi-frequency and pi-amplitude, and show that they are\nequal and satisfy the geometric definition of pi arising from the circumference\nof the circle.\n

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