Hardy’s function Z(t): Results and problems
This is primarily an overview article on some results and problems involving the classical Hardy function Z ( t ):= ζ(1/2 + it )(χ(1/2 + it )) −1/2 , ζ( s ) = χ( s )ζ(1 − s ). In particular, we discuss the first and third moments of Z ( t ) (with and without shifts) and the distribution of its posit...
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| Published in | Proceedings of the Steklov Institute of Mathematics Vol. 296; no. 1; pp. 104 - 114 |
|---|---|
| Main Author | |
| Format | Journal Article Conference Proceeding |
| Language | English |
| Published |
Moscow
Pleiades Publishing
2017
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
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| Summary: | This is primarily an overview article on some results and problems involving the classical Hardy function
Z
(
t
):= ζ(1/2 +
it
)(χ(1/2 +
it
))
−1/2
, ζ(
s
) = χ(
s
)ζ(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. |
|---|---|
| ISSN: | 0081-5438 1531-8605 |
| DOI: | 10.1134/S0081543817010084 |