15 citations · 20 across the 5 of their papers we have counts for
6 papers · 1 filter
On the asymptotic distribution of zeros of modular forms
Zeev Rudnick
We study the distribution of zeros of holomorphic modular forms. Assuming the Generalized Riemann Hypothesis we show that the zeros of Hecke eigenforms for the modular group become…
On the distribution of matrix elements for the quantum cat map
P. Kurlberg, Z. 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 phas…
Linear statistics of low-lying zeros of L--functions
C. P. Hughes, Z. Rudnick
We consider linear statistics of the scaled zeros of Dirichlet --functions, and show that the first few moments converge to the Gaussian moments. The number of Gaussian moments…
Torsion points on curves and common divisors of a^k-1 and b^k-1
Nir Ailon, Zeev Rudnick
We study the behavior of the greatest common divisor of a^k-1 and b^k-1, where a,b are fixed integers or polynomials, and k varies. In the integer case, we conjecture that when a a…
The distribution of spacings between fractional parts of lacunary sequences
Zeev Rudnick, Alexandru Zaharescu
Given an increasing sequence of integers a(n), it is known (due to Weyl) that for almost all reals t, the fractional parts of the dilated sequence t*a(n) are uniformly distributed…
On quantum ergodicity for linear maps of the torus
P. Kurlberg, Z. Rudnick
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…