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

Tsz Ho Chan
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Abstract

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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Tsz Ho Chan. 2004-11-22. Lower order terms of the second moment of $S(t)$. https://arxiv.org/abs/math/0411501

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