The Modified Mellin Transform of Powers of the Zeta-function
نویسنده
چکیده
The modified Mellin transform Zk(s) = ∫ ∞ 1 |ζ( 1 2 + ix)|x dx (k ∈ N) 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.
منابع مشابه
On Sums of Integrals of Powers of the Zeta-function in Short Intervals
The modified Mellin transform Zk(s) = ∫ ∞ 1 |ζ( 1 2 + ix)|x dx (k ∈ N) is used to obtain estimates for
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