18 citations · 64 across the 12 of their papers we have counts for
12 papers
Poisson distribution for gaps between sums of two squares and level spacings for toral point scatterers
Tristan Freiberg, Pär Kurlberg, Lior Rosenzweig
We investigate the level spacing distribution for the quantum spectrum of the square billiard. Extending work of Connors--Keating, and Smilansky, we formulate an analog of the Hard…
Superscars in the Seba billiard
Henrik Ueberschaer, Par Kurlberg
We consider the Laplacian with a delta potential (a "point scatterer") on an irrational torus, where the square of the side ratio is diophantine. The eigenfunctions fall into two c…
Non-universality of the Nazarov-Sodin constant
Par Kurlberg, Igor Wigman
We prove that the Nazarov-Sodin constant, which up to a natural scaling gives the leading order growth for the expected number of nodal components of a random Gaussian field, genui…
On the Fixed Points of the Map x -> x^x Modulo a Prime
Pär Kurlberg, Florian Luca, Igor Shparlinski
In this paper, we show that for almost all primes p there is an integer solution x in [2,p-1] to the congruence x^x == x mod p. The solutions can be interpretated as fixed points o…
Quantum Ergodicity for Point Scatterers on Arithmetic Tori
Henrik Ueberschaer, Par Kurlberg
We prove an analogue of Shnirelman, Zelditch and Colin de Verdiere's Quantum Ergodicity Theorems in a case where there is no underlying classical ergodicity. The system we consider…
On the average exponent of elliptic curves modulo p
Tristan Freiberg, Pär Kurlberg
Given an elliptic curve E/Q and a prime p at which E has good reduction, let e_p be the exponent of the group E_p(F_p) of F_p-rational points on the reduction of E modulo p. Under…