The Euler-Riemann zeta function with even arguments in terms of binomial coefficients
type: Item
instance of: scholarly article
title: The Euler-Riemann zeta function with even arguments in terms of binomial coefficients
zbMATH Open document ID: 1546.11118
DOI: 10.1007/978-3-031-51959-8_14
author: Mircea Merca
publication date: 2024-09-25T00:00:00Z
review text: In this paper under review, the author proves that the power sum symmetric functions can be expressed in terms of elementary symmetric functions and obtain an equivalent form of a classical identity (see Theorem 1). Furthermore, he expresses the Euler-Riemann zeta functions \(\zeta(2n)\), \(\zeta(4n)\), \(\zeta(6n)\), \(\zeta(8n)\), \(\zeta(10n)\) and \(\zeta(12n)\) in terms of binomial coefficients as sums over all integer partitions of the positive integer \(n\) (see Corollaries 1--12).\N\NFor the entire collection see [Zbl 1539.11005].
Mathematics Subject Classification ID: 11M06
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11B68
zbMATH DE Number: 7918583
zbMATH Keywords: Riemann zeta function
zbMATH Keywords: symmetric functions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7918583