https://doi.org/10.4169/amer.math.monthly.121.03.229 https://www.jstor.org/stable/10.4169/amer.math.monthly.121.03.229 Abstract We first present the corrected ...

Universality theorems occupy a central role in analytic number theory, demonstrating that families of analytic functions—including the prototypical Riemann zeta-function—can approximate an extensive ...

We prove that a series derived using Euler's transformation provides the analytic continuation of ζ(s) for all complex s ≠ 1. At negative integers the series becomes a finite sum whose value is given ...

The Riemann Hypothesis, a central unsolved problem in mathematics, posits that all non-trivial zeros of the Riemann zeta function lie on the critical line in the complex plane. This conjecture is not ...