Lower order terms of the second moment of $S(t)$

Details Lower order terms of the second moment of $S(t)$ Lower order terms of the second moment of $S(t)$

2004-11-22

arxiv.org/abs/math/0411501v1

Mathematics

Number Theory

19 pages

Scientific paper

In this article, we derive an asymptotic formula for the second moment of
$S(t)$ which includes the lower order terms using a prediction from the ratios
conjecture of Conrey, Farmer and Zirnbauer. The formula matches very well with
actual values of the second moment.

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