THE DYNAMICAL MORDELL-LANG CONJECTURE (2009)
Robert L. Benedetto, Dragos Ghioca, Pär Kurlberg, J. Tucker
Abstract. We prove a special case of a dynamical analogue of the classical Mordell-Lang conjecture. In particular, let φ be a rational function with no superattracting periodic points other than...
A GAP PRINCIPLE FOR DYNAMICS (2009)
Robert L. Benedetto, Dragos Ghioca, Pär Kurlberg, Thomas J. Tucker
Abstract. Let f1,..., fg ∈ C(z) be rational functions, let Φ = (f1,..., fg) denote their coordinatewise action on (P1) g, let V ⊂ (P1) g be a proper subvariety, and let P = (x1,..., xg) ∈ (P1)...
THE DISTRIBUTION OF SPACINGS BETWEEN QUADRATIC RESIDUES (2009)
The Erwin, Schrödinger International Boltzmanngasse, Pär Kurlberg, Zeév Rudnick, Pär Kurlberg, Zeév Rudnick
Abstract. We study the distribution of spacings between squares modulo q, where q is square-free and highly composite, in the limit as the number of prime factors of q goes to infinity. We show that...
THE BOLTZMANN EQUATION ON A TWO-DIMENSIONAL LATTICE THEORETICAL AND NUMERICAL RESULTS (2008)
Laura Fainsilber, Pär Kurlberg, Bernt Wennberg, Laura Fainsilber, Pär Kurlberg, Bernt Wennberg
ABSTRACT. The construction of discrete velocity models or numerical methods for the Boltzmann equation, may lead to the necessity of computing the collision operator as a sum over lattice points. The...
sis A Local Riemann Hypothesis, II (2008)
In [3], Bump and Ng made the remarkable discovery that the zeroes of the Mellin transform of Hermite functions of even level lie on the critical line Re(s) = 1/2. Hermite functions are eigenfunctions...
PRELIMINARY VERSION ON THE ORDER OF UNIMODULAR MATRICES MODULO INTEGERS (2008)
Abstract. Assuming the Generalized Riemann Hypothesis, we prove the following: If b is an integer greater than one, then the multiplicative order of b modulo N is larger than N 1−ɛ for all N in a...
On the period of the linear congruential and power generators (2008)
We consider two standard pseudorandom number generators from number theory: the linear congruential generator and the power generator. For the former, we are given integers e, b, n (with e, n> 1)...
LATTICE POINTS ON CIRCLES AND DISCRETE VELOCITY MODELS FOR THE BOLTZMANN EQUATION (2008)
Laura Fainsilber, Pär Kurlberg, Bernt Wennberg
The phase space density f of a dilute gas evolves according to the Boltzmann equation. In the physically relevant case, the gas would be confined to a subset Ω ⊂ R 3, and then f(x, v, t) : Ω×R...
ON THE DISTRIBUTION OF MATRIX ELEMENTS FOR THE QUANTUM CAT MAP (2008)
Abstract. For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space...
ON A CHARACTER SUM PROBLEM OF H. COHN (2008)
Abstract. Let f be a complex valued function on a finite field F such that f(0) = 0, f(1) = 1, and |f(x) | = 1 for x � = 0. Cohn asked if it follows that f is a nontrivial multiplicative character...
On the distribution of matrix elements for the quantum cap map (2005)
For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space average of...
On the distribution of matrix elements for the quantum cap map (2005)
For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space average of...
On the Distribution of Matrix Elements for the Quantum Cat Map (2003)
P Ar, Zeév Rudnick, Pär Kurlberg, Ze Ev Rudnick
For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space average of...
Value distribution for eigenfunctions of desymmetrized quantum maps (2001)
Abstract. We study the value distribution and extreme values of eigenfunctions for the “quantized cat map”. This is the quantization of a hyperbolic linear map of the torus. In a previous paper...
On quantum ergodicity for linear maps of the torus (2001)
Abstract. We prove a strong version of quantum ergodicity for linear hyperbolic maps of the torus (“cat maps”). We show that there is a density one sequence of integers so that as N tends to...
Value distribution for eigenfunctions of desymmetrized quantum maps (2001)
We study the value distribution and extreme values of eigenfunctions for the “quantized cat map.” This is the quantization of a hyperbolic linear map of the torus. In a previous paper it was...
Hecke theory and equidistribution for the quantization of linear maps of the torus (1999)
Abstract. We study semi-classical limits of eigenfunctions of a quantized linear hyperbolic automorphism of the torus (“cat map”). For some values of Planck’s constant, the spectrum of the...
The distribution of spacings between quadratic residues (1999)
Abstract. We study the distribution of spacings between squares in Z/QZ as the number of prime divisors of Q tends to infinity. In [3] Kurlberg and Rudnick proved that the spacing distribution for...
The distribution of spacings between quadratic residues (1999)
Abstract. We study the distribution of spacings between squares modulo q, where q is square-free and highly composite, in the limit as the number of prime factors of q goes to infinity. We show that...
The Distribution of Spacings Between Quadratic Residues (1998)
We study the distribution of spacings between squares modulo q, where q is square-free and highly composite, in the limit as the number of prime factors of q goes to infinity. We show that all...
On the Order of Unimodular Matrices Modulo Integers (1991)
Assuming the Generalized Riemann Hypothesis, we prove the following: If b is an integer greater than one, then the multiplicative order of b modulo N is larger than N for all N in a density one...
Daniel Bump, Kwok-Kwong Choi, Pär Kurlberg, P Ar Kurlberg, Jeffrey Vaaler
this paper and its companion piece by Kurlberg [19]. If F = R, we will prove an extension of this result to the harmonic oscillator in n-