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 ...

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 ...

Analytic number theory continues to serve as a cornerstone of modern mathematics through its probing study of zeta functions and their applications. At the heart of this discipline is the classical ...

This article is more than 8 years old. So what? Riemann was interested in the distribution of prime numbers and he discovered a formula for the number of primes less than or equal to a given integer ...

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 ...