Hardy-Ramanujan Journal |
We show that a certain modified Mellin transform M(s) of Hardy's function is an entire function. There are reasons to connect M(s) with the function ζ(2s−1/2), and then the orders of M(s) and ζ(s) should be comparable on the critical line. Indeed, an estimate for M(s) is proved which in the particular case of the critical line coincides with the classical estimate of the zeta-function.