10.46298/hrj.2010.169
https://hrj.episciences.org/169
Jutila, Matti
Matti
Jutila
An estimate for the Mellin transform of powers of Hardy's function.
We show that a certain modified Mellin transform $\mathcal M(s)$ of Hardy's function is an entire function. There are reasons to connect $\mathcal M(s)$ with the function $\zeta(2s-1/2)$, and then the orders of $\mathcal M(s)$ and $\zeta(s)$ should be comparable on the critical line. Indeed, an estimate for $\mathcal M(s)$ is proved which in the particular case of the critical line coincides with the classical estimate of the zeta-function.
episciences.org
Hardy's function
Riemann's zeta-function
Mellin transform
[MATH] Mathematics [math]
2015-06-12
2010-01-01
2010-01-01
en
journal article
https://hal.archives-ouvertes.fr/hal-01112386v1
2804-7370
https://hrj.episciences.org/169/pdf
VoR
application/pdf
Hardy-Ramanujan Journal
Volume 33 - 2010
Researchers
Students