The Connection between the Zeros of the ...-Function and Sequences (g(p)), p Prime, mod 1.
The critical values of certain Dirichlet series.
The cubic moment of central values of automorphic -functions.
The derivative of p-adic L-functions
The distribution and moments of the error term in the Dirichlet divisor problem
The duality of cusp singularities.
The Euler characteristic of the moduli space of curves.
The first moment of quadratic Dirichlet L-functions
The group structure for ζ(3)
The growth rate of the Dedekind Zeta-function on the critical line
The joint universality and the generalized strong recurrence for Dirichlet L-functions
The k-functions in multiplicative number theory. I. On complex explicit formulae
The k-functions in multiplicative number theory. II. Uniform distribution of zeta zeros
The k-functions in multiplicative number theory. III. Uniform distribution of zeta zeros; discrepancy
The k-functions in multiplicative number theory. IV. On a method of A. E. Ingham
The k-functions in multiplicative number theory. V. Changes of sign of some arithmetical error terms
The lowest zero of sections of the zeta function.
The mean square of the divisor function
Let d(n) be the divisor function. In 1916, S. Ramanujan stated without proof that , where P(y) is a cubic polynomial in y and , with ε being a sufficiently small positive constant. He also stated that, assuming the Riemann Hypothesis (RH), . In 1922, B. M. Wilson proved the above result unconditionally. The direct application of the RH would produce . In 2003, K. Ramachandra and A. Sankaranarayanan proved the above result without any assumption. In this paper, we prove .
The mean square of the Riemann zeta-function in the critical strip III
The mean square of the Riemann zeta-function in the critical strip II