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…
2 Citations
On the universality of the Epstein zeta function
- MathematicsCommentarii Mathematici Helvetici
- 2020
We study universality properties of the Epstein zeta function $E_n(L,s)$ for lattices $L$ of large dimension $n$ and suitable regions of complex numbers $s$. Our main result is that, as $n\to\infty$,…
Adelic Rogers integral formula
- Mathematics
- 2022
. We formulate and prove the extension of the Rogers integral formula ([23]) to the adeles of number fields. We also prove the second moment formulas for a few important cases, enabling a number of…
References
SHOWING 1-10 OF 34 REFERENCES
On the Poisson distribution of lengths of lattice vectors in a random lattice
- Mathematics
- 2010
We prove that the volumes determined by the lengths of the non-zero vectors ±x in a random lattice L of covolume 1 define a stochastic process that, as the dimension n tends to infinity, converges…
Lattice point problems and distribution of values of quadratic forms
- Mathematics
- 1999
For d-dimensional irrational ellipsoids E with d > 9 we show that the number of lattice points in rE is approximated by the volume of rE, as r tends to infinity, up to an error of order o(rd-2). The…
Convergence of probability measures
- Mathematics
- 2011
The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the…
The minima of quadratic forms and the behavior of Epstein and Dedekind zeta functions
- Mathematics
- 1980
Stable non-Gaussian random processes
- Mathematics
- 1994
The asymptotic behaviour of (Yn, n e N) is of fundamental importance in probability theory. Indeed, if the Xj have common mean fi and variance a, then by taking each an = n/u and b„ = n a, the…
On the zeros of Epstein's zeta function
- Mathematics
- 1967
Let Q ( x, y ) = ax 2 + bxy + cy 2 be a positive definite quadratic form with discriminant d = b 2 – 4 ac . The Epstein zeta function associated with Q is given by where Σ′ means the sum is over all…
Poisson Processes
- MathematicsInternational Encyclopedia of Statistical Science
- 2011
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.
Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance
- Mathematics
- 1995
Stable random variables on the real line Multivariate stable distributions Stable stochastic integrals Dependence structures of multivariate stable distributions Non-linear regression Complex stable…
Mathematische Werke
- HistoryNature
- 1948
VERSATILITY is the most delusive of the fairy gifts ; the men of genius on whom it was bestowed otherwise than in subtle malevolence can be counted on the fingers. In the age of Euler himself, Johann…
Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse
- Mathematics
- 2013
Meinen Dank für die Auszeichnung, welche mir die Akademie durch die Aufnahme unter ihre Correspondenten hat zu Theil werden lassen, glaube ich am besten dadurch zu erkennen zu geben, dass ich von der…