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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

Trudy Mat. Inst. Steklova, 2017 Volume 296, Pages 111–122 (Mi tm3778)

This article is cited in 2 papers

Hardy's function $Z(t)$: Results and problems

A. Ivić

Serbian Academy of Sciences and Arts, Beograd, Serbia

Abstract: This is primarily an overview article on some results and problems involving the classical Hardy function $Z(t) := \zeta (1/2+it)(\chi (1/2+it))^{-1/2}$, $\zeta (s) = \chi (s)\zeta (1-s)$. In particular, we discuss the first and third moments of $Z(t)$ (with and without shifts) and the distribution of its positive and negative values. A new result involving the distribution of its values is presented.

UDC: 511.323+511.346+517.518

Received: January 13, 2016

DOI: 10.1134/S0371968517010083


 English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 296, 104–114

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