15 citations · 20 across the 5 of their papers we have counts for
12 papers
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…
Eigenvalue spacings for regular graphs
D. Jakobson, S. D. Miller, I. Rivin +1
We carry out a numerical study of fluctuations in the spectrum of regular graphs. Our experiments indicate that the level spacing distribution of a generic k-regular graph approach…
On the distribution of lattice points in thin annuli
C. P. Hughes, Z. Rudnick
We show that the number of lattice points lying in a thin annulus has a Gaussian value distribution if the width of the annulus tends to zero sufficiently slowly as we increase the…
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…