THE SECOND MOMENT OF THE RIEMANN ZETA FUNCTION WITH UNBOUNDED SHIFTS

On the second moment of S(T ) in the theory of the Riemann zeta function

We assume the Riemann Hypothesis and an quantitative form of the Twin Prime Conjecture, and obtain an asymptotic formula for the second moment of S(T ) with better error term.

The Twisted Fourth Moment of the Riemann Zeta Function

We compute the asymptotics of the fourth moment of the Riemann zeta function times an arbitrary Dirichlet polynomial of length T 1 11 −ε.

Mollifying the Riemann Zeta-function

Lagrangians with Riemann Zeta Function

We consider construction of some Lagrangians which contain the Riemann zeta function. The starting point in their construction is p-adic string theory. These Lagrangians describe some nonlocal and nonpolynomial scalar field models, where nonlocality is controlled by the operator valued Riemann zeta function. The main motivation for this research is intention to find an effective Lagrangian for ...

The Theory of the Riemann Zeta-function