On the value distribution and moments of the Epstein zeta function to the right of the critical strip

• We study the Epstein zeta function E-n(L, S) for s > n/2 and a random lattice L of large dimension n. For any fixed c > 1/2 we determine the value distribution and moments of E-n(., cn) (suitably normalized) as n -> infinity. We further discuss the random function C -> E-n(., cn) for c is an element of [A, B] with 1/2 < A < B and determine its limit distribution as n -> infinity.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Lattices

Epstein's zeta function

Value distribution

Moments

MATHEMATICS

MATEMATIK

Mathematics

Matematik

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