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

Carl Anders Södergren

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

Carl Anders Södergren

Department of Mathematical Sciences

4 Citations (Scopus)

Abstract

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→∞. We further discuss the random function c E_n(.,cn) for c∈[A,B] with 1/2<A<B and determine its limit distribution as n→∞.

Original language	English
Journal	Journal of Number Theory
Volume	131
Issue number	7
Pages (from-to)	1176-1208
ISSN	0022-314X
Publication status	Published - Jul 2011

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abstract = "We study the Epstein zeta function En(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 En(.,cn) (suitably normalized) as n→∞. We further discuss the random function c En(.,cn) for c∈[A,B] with 1/2<A<B and determine its limit distribution as n→∞.",

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N2 - We study the Epstein zeta function En(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 En(.,cn) (suitably normalized) as n→∞. We further discuss the random function c En(.,cn) for c∈[A,B] with 1/2<A<B and determine its limit distribution as n→∞.

AB - We study the Epstein zeta function En(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 En(.,cn) (suitably normalized) as n→∞. We further discuss the random function c En(.,cn) for c∈[A,B] with 1/2<A<B and determine its limit distribution as n→∞.

M3 - Journal article

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VL - 131

SP - 1176

EP - 1208

JO - Journal of Number Theory

JF - Journal of Number Theory

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ER -

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

Abstract

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