The two dimensional distribution of values of $ζ(1+it)$

Details The two dimensional distribution of values of $ζ(1+it)$ The two dimensional distribution of values of $ζ(1+it)$

2008-01-24

arxiv.org/abs/0801.3692v2

Int Math Res Notices, IMRN (2008), article ID rnn106

Mathematics

Number Theory

40 pages

Scientific paper

We prove several results on the distribution function of $\zeta(1+it)$ in the
complex plane, that is the joint distribution function of $\arg\zeta(1+it)$ and
$|\zeta(1+it)|$. Similar results are also given for $L(1,\chi)$ (as $\chi$
varies over non-principal characters modulo a large prime $q$).

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