Matti Jutila

Uniform bound for Hecke L-functions

Our principal aim in the present article is to establish a uniform hybrid bound for individual values on the critical line of Hecke

Riemann’s zeta-function and the divisor problem. III

L

Primes in short intervals

-functions associated with cusp forms over the full modular group. This is rendered in the statement that for

On character sums and class numbers

t\ge0

Transformation formulae for Dirichlet polynomials

\eqalignno{H_j(\txt{1\over2}+it)&\ll(\kappa_j+t)^{1/3+\epsilon},&(1.1)\cr H_{j,k}(\txt{1\over2}+it)&\ll (k+t)^{1/3+\epsilon},&(1.2)\cr}

GAPS BETWEEN THE ZEROS OF EPSTEIN'S ZETA-FUNCTIONS ON THE CRITICAL LINE

with the common notation to be made precise in the course of discussion. Talks on this and relevant results were delivered by the authors at MF Oberwolfach on September 20, 2004, and at General Assembry of Math. Soc. Japan on March 30, 2005.

Gaps Between Consecutive Zeros of the Riemann Zeta-Function on the Critical Line.

In two earlier papers with the same title, we studied connections between Voronoi’s formula in the divisor problem and Atkinson’s formula for the mean square of Riemann’s zeta-function. Now we consider this correspondence in terms of segments of sums appearing in these formulae and show that a certain arithmetic conjecture concerning the divisor function implies best possible bounds for the classical error terms Δ(x) and E(T).