108 citations · 552 across the 31 of their papers we have counts for
4 papers · 2 filters
Distjointness of Mobius from horocycle flows
Jean Bourgain, Peter Sarnak, Tamar Ziegler
We formulate and prove a finite version of Vinogradov's bilinear sum inequality. We use it together with Ratner's joinings theorems to prove that the Mobius function is disjoint fr…
The horocycle flow at prime times
P. Sarnak, A. Ubis
We prove that the orbit of a non-periodic point at prime values of the horocycle flow in the modular surface is dense in a set of positive measure. For some special orbits we also…
Affine Sieve
Alireza Salehi Golsefidy, Peter Sarnak
We establish the main saturation conjecture in [BGS10] connected with executing a Brun sieve in the setting of an orbit of a group of affine linear transformations. This is carried…
Real zeros of holomorphic Hecke cusp forms
Amit Ghosh, Peter Sarnak
This note is concerned with the zeros of holomorphic Hecke cusp forms of large weight on the modular surface. The zeros of such forms are symmetric about three geodesic segments an…