On the value distribution of the Epstein zeta function in the critical strip

@inproceedings{Sodergren2011OnTV,
  title={On the value distribution of the Epstein zeta function in the critical strip},
  author={Anders Sodergren},
  year={2011}
}
We study the value distribution of the Epstein zeta function En(L, s) for 0 < s < n 2 and a random lattice L of large dimension n. For any fixed c ∈ ( 1 4 , 1 2 ) and n → ∞, we prove that the random variable V −2c n En(·, cn) has a limit distribution, which we give explicitly (here Vn is the volume of the ndimensional unit ball). More generally, for any fixed ε > 0 we determine the limit distribution of the random function c 7→ V −2c n En(·, cn), c ∈ [ 1 4 + ε, 1 2 − ε]. After compensating for… 

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    International Encyclopedia of Statistical Science
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TLDR
Consider a Random Process that models the occurrence and evolution of events in time and the random variable N(t) which represents the largest n, such that Sn( t) ≤ t.