The modified Mellin transform of powers of the zeta-function
Ivić, Aleksandar
Original · EN
The modified Mellin transform Zₖ(s) = ∫₁∞ |ζ(1/2+ix)|²ᵏx⁻ˢ d x (k = 1,2,...) is investigated. Analytic continuation and mean square estimates of Zₖ(s) are discussed, as well as connections with power moments of |ζ(1/2+ix)|, with the special emphasis on the cases k = 1,2.
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