3 papers
math.NT2025
Some series equivalent to the extended Riemann hypothesis for Dedekind zeta functions
Vincent Nguyen
The extended Riemann hypothesis (ERH) for Dedekind zeta functions remains one of the most elusive open problems in number theory. Over the last century, many equivalent statements…
math.NT2025
A series involving a product of four consecutive harmonic numbers
Wilson J. Chen, Vincent Nguyen
In correspondence with Goldbach, Euler began investigating series of the form , which are known today as Euler sums…
math.CA2024
On Some Series Involving Harmonic and Skew-Harmonic Numbers
Vincent Nguyen
In this paper, we evaluate in closed form several different series involving the harmonic numbers and skew-harmonic numbers. We consider two classes of series involving these seque…