This paper follows the article in [1] which presents a geometric interpretation of the Dirichlet eta function, and presents an analysis of the zeros of the eta function in that context. In that paper, a modified eta function, with summation to N, arbitrarily large, was used.

In this paper, the eta function with summation to infinity is cast into an infinite-dimensional Hilbert space, demonstrating that the geometric logic in [1] still applies.

The analysis of the properties of the eta function, and the geometric constraints on the structures representing it, shows that it can have at most one zero in the critical strip for any given imaginary value of its complex argument s.

k-dominating set, k-domination number, 2-dominating set, 2‑domination number, Cartesian product graphs, cycles.

Received: January 1, 2021; Accepted: January 13, 2021; Published: Januray 30, 2021

How to cite this article: Mike Kelly, The Dirichlet eta function in an infinite-dimensional Hilbert space, Universal Journal of Mathematics and Mathematical Sciences 14(1) (2021), 9-12. DOI: 10.17654/UM014010009

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License 

References:

[1] M. Kelly, The geometry of the Dirichlet eta function, Far East Journal of Mathematical Sciences (FJMS) 128(1) (2021), 1-13.
[2] https://en.wikipedia.org/wiki/Dirichlet_eta_function
[3] https://en.wikipedia.org/wiki/Hilbert_space