Vorrapan Chandee

Bounding |ζ(½+it)| on the Riemann hypothesis

In 1924 Littlewood showed that, assuming the Riemann Hypothesis, for large t there is a constant C such that |\zeta(1/2+it)| \ll \exp(C\log t/\log \log t). In this note we show how the problem of bounding |\zeta(1/2+it)| may be framed in terms of minorizing the function \log ((4+x^2)/x^2) by functions whose Fourier transforms are supported in a given interval, and drawing upon recent work of Carneiro and Vaaler we find the optimal such minorant. Thus we establish that any C> (\log 2)/2 is permissible in Littlewoods result.

Bounding \(S(t)\) and \(S_1(t)\) on the Riemann hypothesis

Let

EXPLICIT UPPER BOUNDS FOR L-FUNCTIONS ON THE CRITICAL LINE

\pi S(t)

Group Structures of Elliptic Curves Over Finite Fields

denote the argument of the Riemann zeta-function,

On the correlation of shifted values of the Riemann zeta function

\zeta (s)

Trilinear forms with Kloosterman fractions

, at the point