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

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.

DOI: https://doi.org/10.1134/S0371968517010083

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

Bibliographic databases:

UDC: 511.323+511.346+517.518
Received: January 13, 2016

Citation: A. Ivić, “Hardy's function $Z(t)$: Results and problems”, Analytic and combinatorial number theory, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov, Tr. Mat. Inst. Steklova, 296, MAIK Nauka/Interperiodica, Moscow, 2017, 111–122; Proc. Steklov Inst. Math., 296 (2017), 104–114

Citation in format AMSBIB
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\paper Hardy's function $Z(t)$: Results and problems
\inbook Analytic and combinatorial number theory
\bookinfo Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov
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\yr 2017
\vol 296
\pages 111--122
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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