Stephen Lester

A note on simple a-points of L-functions

We prove, subject to certain hypotheses, that a positive proportion of the a-points of the Riemann zeta-function and Dirichlet L-functions with primitive characters are simple and discuss corresponding results for other functions in the Selberg class. We also prove an unconditional result of this type for the a-points in fixed strips to the right of the line s = 1/2.

On the distribution of the divisor function and Hecke eigenvalues

We investigate the behavior of the divisor function in both short intervals and in arithmetic progressions. The latter problem was recently studied by É. Fouvry, S. Ganguly, E. Kowalski and Ph. Michel. We prove a complementary result to their main theorem. We also show that in short intervals of certain lengths the divisor function has a Gaussian limiting distribution. The analogous problems for Hecke eigenvalues are also considered.

a-Points of the Riemann Zeta-Function on the Critical Line

We investigate the proportion of the nontrivial roots of the equation

Small Scale Equidistribution of Eigenfunctions on the Torus

\zeta (s)=a

MEAN VALUES OF ζ′/ζ(s), CORRELATIONS OF ZEROS AND THE DISTRIBUTION OF ALMOST PRIMES

, which lie on the line

On the variance of sums of divisor functions in short intervals

\Re s=1/2

Zeros of Modular Forms in Thin Sets and Effective Quantum Unique Ergodicity

for

THE DISTRIBUTION OF THE LOGARITHMIC DERIVATIVE OF THE RIEMANN ZETA-FUNCTION

a \in \mathbb C

Small scale distribution of zeros and mass of modular forms

not equal to zero. We show that at most one-half of these points lie on the line

On the distribution of the zeros of the derivative of the Riemann zeta-function

\Re s=1/2