Numbers like π, e and φ often turn up in unexpected places in science and mathematics. Pascal’s triangle and the Fibonacci sequence also seem inexplicably widespread in nature. Then there’s the ...

The Riemann hypothesis is equivalent to the Li criterion governing a sequence of real constants $\{\lambda _{k}\}_{k=1}^{\infty}$ that are certain logarithmic derivatives of the Riemann xi function ...

We present one-parameter series representations for the following series involving the Riemann zeta function∑n=3nodd∞ζ(n)nsnand∑n=2neven∞ζ(n)nsnand we apply our results to obtain new representations ...

The Riemann zeta function, a central object in analytic number theory, has long intrigued mathematicians and physicists alike. Its non-trivial zeros not only encapsulate the distribution of prime ...

The Riemann Hypothesis remains one of mathematics’ most enduring and influential conjectures, proposing that all nontrivial zeros of the Riemann zeta function lie on the critical line where the real ...

Numbers like pi, e and phi often turn up in unexpected places in science and mathematics. Pascal's triangle and the Fibonacci sequence also seem inexplicably widespread in nature. Then there's the ...