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

TY - JOUR

T1 - On the value distribution and moments of the Epstein zeta function to the right of the critical strip

AU - Södergren, Carl Anders

PY - 2011/7

Y1 - 2011/7

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

SN - 0022-314X

VL - 131

SP - 1176

EP - 1208

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 7

ER -