Higher moments of the Epstein zeta functions
نویسنده
چکیده
holds as T → ∞. The basic tools of them are the approximate functional equations for ζ(s) and ζ(s). Therefore, one might think that we can obtain the asymptotic formula for the higher moments (sixth moment, eighth moment, etc· · · ) of ζ(s) on the critical line Re(s) = 12 by using the approximate functional equations for ζ(s) (k ≥ 3). However, although these approximate functional equations are known, a straightforward application of them doesn’t give the desirable results. In fact, it is generally conjectured that ∫ T
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