Hybrid Moments of the Riemann Zeta-function
نویسنده
چکیده
The “hybrid” moments Z 2T T |ζ( 1 2 + it)| „ Z t+G t−G |ζ( 1 2 + ix)| dx m dt of the Riemann zeta-function ζ(s) on the critical line Re s = 1 2 are studied. The expected upper bound for the above expression is Oε(T G). This is shown to be true for certain specific values of k, l,m ∈ N, and the explicitly determined range of G = G(T ; k, l,m). The application to a mean square bound for the Mellin transform function of |ζ( 1 2 + ix)| is given.
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