Home Sum formula of multiple Hurwitz-zeta values
Article
Licensed
Unlicensed Requires Authentication

Sum formula of multiple Hurwitz-zeta values

  • Jianqiang Zhao EMAIL logo
Published/Copyright: February 22, 2013
Forum Mathematicum
From the journal Forum Mathematicum Volume 27 Issue 2

Abstract

Let s1,⋯,sd be d positive integers and define the multiple t-values of depth d by

t(s1,⋯,sd)=∑n1>⋯>nd≥11(2n1-1)s1⋯(2nd-1)sd,

which is equal to the multiple Hurwitz-zeta value 2-wζ(s1,⋯,sd;-12,⋯,-12) where w=s1+⋯+sd is called the weight. For d≤n, let T(2n,d) be the sum of all multiple t-values with even arguments whose weight is 2n and whose depth is d. In 2011, Shen and Cai gave formulas for T(2n,d) for d≤5 in terms of t(2n), t(2)t(2n-2) and t(4)t(2n-4). In this short note we generalize their results to arbitrary depth by using the theory of symmetric functions established by Hoffman (2012).

Keywords: Multiple Hurwitz-zeta values; multiple zeta functions; symmetric functions; generating functions; recursive systems of DE
MSC: 11M32; 11M35; 05A15

Funding source: NSF

Award Identifier / Grant number: DMS1162116

This work was started while the author was visiting Taida Institute for Mathematical Sciences at National Taiwan University in the summer of 2012. He would like to thank Profs. Jing Yu and Chieh-Yu Chang for encouragement and their interest in his work. The author is partially supported by NSF grant DMS1162116.

Received: 2012-9-26
Published Online: 2013-2-22
Published in Print: 2015-3-1

© 2015 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Near abelian profinite groups
  3. On Calabi–Yau threefolds associated to a web of quadrics
  4. On the partial fraction decomposition of the restricted partition generating function
  5. Projectively flat Finsler manifolds with infinite dimensional holonomy
  6. Weighted version of Carleson measure and multilinear Fourier multiplier
  7. Injective objects and retracts of Fraïssé limits
  8. On hypersurfaces containing projective varieties
  9. Additive reducts of algebraically closed valued fields
  10. On the subconvexity problem for GL(3) × GL(2) L-functions
  11. An algebraic property of Hecke operators and two indefinite theta series
  12. Sum formula of multiple Hurwitz-zeta values
  13. Classification of homogeneous holomorphic hermitian principal bundles over G/K
  14. Integrality properties of the CM-values of certain weak Maass forms
  15. Heat kernel for fractional diffusion operators with perturbations
  16. New class of multiple weights and new weighted inequalities for multilinear operators
  17. Balanced Hermitian geometry on 6-dimensional nilmanifolds
  18. Extensions of tame algebras and finite group schemes of domestic representation type
  19. Weighted estimates for multilinear Fourier multipliers
  20. Cluster tilting vs. weak cluster tilting in Dynkin type A infinity
  21. From ring epimorphisms to universal localisations
  22. Brauer algebras of type B
  23. Existence problems for the p-Laplacian
  24. Averaging operators over nondegenerate quadratic surfaces in finite fields
  25. Lawson homology for abelian varieties
https://doi.org/10.1515/forum-2012-0144
Keywords for this article
Multiple Hurwitz-zeta values; multiple zeta functions; symmetric functions; generating functions; recursive systems of DE

Articles in the same Issue

  1. Frontmatter
  2. Near abelian profinite groups
  3. On Calabi–Yau threefolds associated to a web of quadrics
  4. On the partial fraction decomposition of the restricted partition generating function
  5. Projectively flat Finsler manifolds with infinite dimensional holonomy
  6. Weighted version of Carleson measure and multilinear Fourier multiplier
  7. Injective objects and retracts of Fraïssé limits
  8. On hypersurfaces containing projective varieties
  9. Additive reducts of algebraically closed valued fields
  10. On the subconvexity problem for GL(3) × GL(2) L-functions
  11. An algebraic property of Hecke operators and two indefinite theta series
  12. Sum formula of multiple Hurwitz-zeta values
  13. Classification of homogeneous holomorphic hermitian principal bundles over G/K
  14. Integrality properties of the CM-values of certain weak Maass forms
  15. Heat kernel for fractional diffusion operators with perturbations
  16. New class of multiple weights and new weighted inequalities for multilinear operators
  17. Balanced Hermitian geometry on 6-dimensional nilmanifolds
  18. Extensions of tame algebras and finite group schemes of domestic representation type
  19. Weighted estimates for multilinear Fourier multipliers
  20. Cluster tilting vs. weak cluster tilting in Dynkin type A infinity
  21. From ring epimorphisms to universal localisations
  22. Brauer algebras of type B
  23. Existence problems for the p-Laplacian
  24. Averaging operators over nondegenerate quadratic surfaces in finite fields
  25. Lawson homology for abelian varieties
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 3.11.2025 from https://www.degruyterbrill.com/document/doi/10.1515/forum-2012-0144/html
Scroll to top button