On some problems involving Hardy's function

Details On some problems involving Hardy's function On some problems involving Hardy's function

2010-10-06

arxiv.org/abs/1010.1073v2

Cent. Eur. J. Math. 8(6)(2010), 1029-1040

Mathematics

Number Theory

15 pages

Scientific paper

10.2478/s11533-010-0071-y

Some problems involving the classical Hardy function $$ Z(t) := \zeta(1/2+it)\bigl(\chi(1/2+it)\bigr)^{-1/2}, \quad \zeta(s) = \chi(s)\zeta(1-s) $$ are discussed. In particular we discuss the odd moments of $Z(t)$, the distribution of its positive and negative values and the primitive of $Z(t)$. Some analogous problems for the mean square of $|\zeta(1/2+it)|$ are also discussed.

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