108 citations · 814 across the 70 of their papers we have counts for
4 papers · 1 filter
Traces of high powers of the Frobenius class in the hyperelliptic ensemble
Zeev Rudnick
The zeta function of a curve over a finite field may be expressed in terms of the characteristic polynomial of a unitary symplectic matrix, called the Frobenius class of the curve.…
The variance of arithmetic measures associated to closed geodesics on the modular surface
Wenzhi Luo, Zeev Rudnick, Peter Sarnak
We determine the variance for the fluctuations of the arithmetic measures obtained by collecting all closed geodesics on the modular surface with the same discriminant and ordering…
The fluctuations in the number of points on a hyperelliptic curve over a finite field
P. Kurlberg, Z. Rudnick
The number of points on a hyperelliptic curve over a field of elements may be expressed as where is a certain character sum. We study fluctuations of as the cur…
Statistics of the zeros of zeta functions in families of hyperelliptic curves over a finite field
Dmitry Faifman, Zeev Rudnick
We study the fluctuations in the distribution of zeros of zeta functions of a family of hyperelliptic curves defined over a fixed finite field, in the limit of large genus. Accordi…