30 research outputs found
High pseudomoments of the Riemann zeta function
The pseudomoments of the Riemann zeta function, denoted ,
are defined as the th integral moments of the th partial sum of
on the critical line. We improve the upper and lower bounds for the
constants in the estimate as
for fixed , thereby determining the two first terms of the
asymptotic expansion. We also investigate uniform ranges of where this
improved estimate holds and when may be lower bounded by the
th power of the norm of the th partial sum of on
the critical line.Comment: This paper has been accepted for publication in Journal of Number
Theor
Sharp upper bounds for fractional moments of the Riemann zeta function
We establish sharp upper bounds for the th moment of the Riemann zeta
function on the critical line, for all real .
This improves on earlier work of Ramachandra, Heath-Brown and
Bettin-Chandee-Radziwi\l\lComment: 10 page