Mean value estimates for exponential sums and L-functions: a spectral theoretic approach.
Mean value estimates for exponential sums with applications to -functions
Mean value results for the approximate functional equation of the square of the Riemann zeta-function
Mean value theorems for long Dirichlet polynomials and tails of Dirichlet series
We obtain formulas for computing mean values of Dirichlet polynomials that have more terms than the length of the integration range. These formulas allow one to compute the contribution of off-diagonal terms provided one knows the correlation functions for the coefficients of the Dirichlet polynomials. A smooth weight is used to control error terms, and this weight can in typical applications be removed from the final result. Similar results are obtained for the tails of Dirichlet series. Four examples...
Mean values of the Riemann zeta-function and its derivatives.
Möbius convolutions and the Riemann hypothesis.
Moments of characteristic polynomials enumerate two-rowed lexicographic arrays.
More than 41% of the zeros of the zeta function are on the critical line
More than two fifths of the zeros of the Riemann zeta function are on the critical line.
Multiple finite Riemann zeta functions
Multiplicity results for the functional equation of the Dirichlet L-functions: case p=2
Multiplicity results for the functional equation of the Dirichlet L-functions