there are still many unanswered questions in analytic number theory, which is the study of the properties of integers and prime numbers. One of the most significant of these questions is the Riemann ...

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 ...

Just 100 years ago the young Bernhard Riemann gave his famed paper on the foundations of geometry. He discussed space of four or more dimensions, and paved the way for the General Theory of ...

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

derivative and Cauchy Riemann conditions, analytic functions, integration in the complex plane, Cauchy's integral formula, infinite series for complex variables. Taylor series, Laurent series, residue ...

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 ...