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

Youness Lamzouri

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

Number Theory 2010-05-26 v2

Authors: Youness Lamzouri

Abstract

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 $q$ ).

Keywords

Riemann zeta function distribution of values joint distribution L-functions Dirichlet characters number theory

Cite

@article{arxiv.0801.3692,
  title  = {The two dimensional distribution of values of $\zeta(1+it)$},
  author = {Youness Lamzouri},
  journal= {arXiv preprint arXiv:0801.3692},
  year   = {2010}
}

Comments

40 pages

Related papers

View all related →