# On some problems involving Hardy’s function

Open Mathematics (2010)

• Volume: 8, Issue: 6, page 1029-1040
• ISSN: 2391-5455

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## Abstract

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Some problems involving the classical Hardy function $Z\left(t\right)=\zeta \left(\frac{1}{2}+it\right){\left(\chi \left(\frac{1}{2}+it\right)\right)}^{-1/\phantom{12}\phantom{\rule{0.0pt}{0ex}}2},\zeta \left(s\right)=\chi \left(s\right)\zeta \left(1-s\right)$ , are discussed. In particular we discuss the odd moments of Z(t) and the distribution of its positive and negative values.

## How to cite

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Aleksandar Ivić. "On some problems involving Hardy’s function." Open Mathematics 8.6 (2010): 1029-1040. <http://eudml.org/doc/269466>.

@article{AleksandarIvić2010,
abstract = {Some problems involving the classical Hardy function $Z\left( t \right) = \zeta \left( \{\frac\{1\}\{2\} + it\} \right)\left( \{\chi \left( \{\frac\{1\}\{2\} + it\} \right)\} \right)^\{ - \{1 \mathord \{\left\bad. \{\vphantom\{1 2\}\} \right. \hspace\{0.0pt\}\} 2\}\} , \zeta \left( s \right) = \chi \left( s \right) \zeta \left( \{1 - s\} \right)$ , are discussed. In particular we discuss the odd moments of Z(t) and the distribution of its positive and negative values.},
author = {Aleksandar Ivić},
journal = {Open Mathematics},
keywords = {Hardy’s function; Riemann zeta-function; Distribution of values; Hardy's function},
language = {eng},
number = {6},
pages = {1029-1040},
title = {On some problems involving Hardy’s function},
url = {http://eudml.org/doc/269466},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Aleksandar Ivić
TI - On some problems involving Hardy’s function
JO - Open Mathematics
PY - 2010
VL - 8
IS - 6
SP - 1029
EP - 1040
AB - Some problems involving the classical Hardy function $Z\left( t \right) = \zeta \left( {\frac{1}{2} + it} \right)\left( {\chi \left( {\frac{1}{2} + it} \right)} \right)^{ - {1 \mathord {\left\bad. {\vphantom{1 2}} \right. \hspace{0.0pt}} 2}} , \zeta \left( s \right) = \chi \left( s \right) \zeta \left( {1 - s} \right)$ , are discussed. In particular we discuss the odd moments of Z(t) and the distribution of its positive and negative values.
LA - eng
KW - Hardy’s function; Riemann zeta-function; Distribution of values; Hardy's function
UR - http://eudml.org/doc/269466
ER -

## References

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