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This article is cited in 2 scientific papers (total 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.
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, Trudy Mat. Inst. Steklova, 296, MAIK Nauka/Interperiodica, Moscow, 2017, 111–122; Proc. Steklov Inst. Math., 296 (2017), 104–114
Linking options:
https://www.mathnet.ru/eng/tm3778https://doi.org/10.1134/S0371968517010083 https://www.mathnet.ru/eng/tm/v296/p111
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Abstract page: | 248 | Full-text PDF : | 72 | References: | 44 | First page: | 12 |
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