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

preprint2008arXivOpen access

Abstract

We prove several results on the distribution function of ζ(1+it)ζ(1+it) in the complex plane, that is the joint distribution function of arg⁡ζ(1+it)\argζ(1+it) and ∣ζ(1+it)∣|ζ(1+it)|. Similar results are also given for L(1,χ)L(1,χ) (as χχ varies over non-principal characters modulo a large prime qq).

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