The Riemann zeta function encodes information about the prime numbers —the atoms of arithmetic and critical to modern cryptography on which e-commerce is built. Finding a proof has been the holy grail ...

However, despite thousands of years of study and great interest, there are still many unanswered questions in analytic number theory, which is the study of the properties of integers and prime numbers ...

quantum modular forms), and analytic number theory (prime distribution, Riemann zeta function, arithmetic functions, arithmetic density). Other active interests include physics (statistical physics, ...

Zeta functions, particularly the Riemann zeta function ... also provides new tools for evaluating sums and series in number theory. Additionally, studies have focused on parametric Euler-type ...

Srinivasa Ramanujan, often referred to as a "mathematical genius", made groundbreaking contributions to areas such as the Riemann series, Divergent Series Theory, elliptic integrals, and ...