5 papers · 1 filter
Bilinear forms with Kloosterman sums via quadratic characters
Valentin Blomer, Alexandru Pascadi
We prove new bounds for bilinear forms with Kloosterman sums, valid for all moduli c. In the critical range where the summation length is the square root of the modulus, the saving…
A GL(3) converse theorem via a "beyond endoscopy" approach
Valentin Blomer, Wing Hong Leung
We give a new proof of the converse theorem for Maass forms on using a technique that is inspired by Langlands' philosophy of "beyond endoscopy", thereby implementing…
The mixing conjecture under GRH
Valentin Blomer, Farrell Brumley, Ilya Khayutin
We prove the Mixing Conjecture of Michel--Venkatesh for the class group action on Heegner points of large discriminant on compact arithmetic surfaces attached to maximal orders in…
The Manin-Peyre conjecture for smooth spherical Fano threefolds
Valentin Blomer, Jörg Brüdern, Ulrich Derenthal +1
The Manin-Peyre conjecture is established for smooth spherical Fano threefolds of semisimple rank one and type N. Together with the previously solved case T and the toric cases, th…
The unipotent mixing conjecture
Valentin Blomer, Philippe Michel
We show that shifted pairs of discrete or continuous low-lying horocycles equidistribute in the product space of two modular curves.