TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Results on Riemann Zeta functions using compositions

, , *

* Corresponding author · click or hover a name for details

pp. 1437–1447Vol. 27Issue 6September 2024DOI: 10.47974/JIM-1903XML
Received:
05 Dec 2023
Published Online:
30 Sep 2024
Article type:
Research Article
Language:
EN
Article no.:
JIM-1903
Pages:
1437–1447

Abstract

The main results of our paper are relations involving sums of Multiple Zeta Riemann functions (MZVs). Using the techniques described here, we found a simple relation for z({a}n) = z(a, a, ..., a^n)  for a positive integer n and a complex a where Re{a} > 1. 

Keywords

Subject Classifications

[2010] 40B0540C1517A42

References

[1] M. Alegri, Identities involving sum of divisors, integer partitions and compositions, Online J. Anal. Comb., 17, Article Number 3, 29 Pages (2023).
[2] M. Alegri, Identities involving sum of divisors, compositions and integer partitions hiding in the q-binomial theorem, São Paulo J. Math. Sci., 18, 1-13 (2024).
[3] M. Alegri and E. V. P. Spreafico, On series involving sine, cosine, and k-colored partition function, Indian J. Pure Appl. Math., (2024). https://doi.org/10.1007/s13226-024-00534-2.
[4] G. E. Andrews, R. Askey and R. Roy, Special Functions, Cambridge University Press, London, (1999).
[5] V. K. Balakrishnan, Introductory Discrete Mathematics, Englewood Cliffs, NJ: Prentice Hall, (1991).
[6] J. M. Borwein and R. Girgensohn, Evaluation of triple Euler sums, Electron. J. Comb., 3(1), Research paper R23, 27 Pages (1996).
[7] J. Burgos and J. Frésan, Multiple Zeta values: from numbers to motives, Clay Mathematics Proceedings, American Mathematical Society, Providence, RI, (2017).
[8] Ch. A. Charalambides, Enumerative combinatorics, Chapman & Hall, CRC Press Company, Boca Raton, London, New York, Washington, D.C., (2002).
[9] S. Heubach and T. Mansour, Compositions of n with parts in a set, Congr. Numerantium, 168, 127-143 (2004).
[10] M. E. Hoffman, Multiple harmonic series, Pac. J. Math. 152(2), 275-290 (1992).
[11] R. Sita Ramachandra Rao and M. V. Subbarao, Transformation formulae for multiple series, Pac. J. Math., 113, 471-479 (1984).
[12] A. V. Sills, Compositions, partitions, and Fibonacci numbers, Fibonacci Q., 49(4), 348-354 (2011).
[13] D. Zagier, Evaluation of the multiple Zeta values ζ(2, …, 2, 3, 2, …, 2), Ann. Math. (2), 175(2), 977-1000 (2012).
[14] D. Zagier, Values of Zeta functions and their applications, in: Joseph, A. (ed.) et al., First European congress of mathematics (ECM), Paris, France, July 6-10, 1992, Volume II: Invited lectures (Part 2), Basel: Birkhäuser, Prog. Math., 120, 497-512 (1994).

Views: 329Downloads: 79Citations: 1