Sparse equidistribution problems, period bounds, and subconvexity
Akshay Venkatesh
Abstract
We introduce a ``geometric'' method to bound periods of automorphic forms. The key features of this method are the use of equidistribution results in place of mean value theorems, and the systematic use of mixing and the spectral gap. Applications are given to equidistribution of sparse subsets of horocycles and to equidistribution of CM points; to subconvexity of the triple product period in the level aspect over number fields, which implies subconvexity for certain standard and Rankin-Selberg L-functions; and to bounding Fourier coefficients of automorphic forms.
Create a lesson
Related papers
Value distribution of multiplicative functions along linear fractional sequences
Sun-Kai Leung
Delta theory of Anderson Modules II: Hodge-Pink structure
Sudip Pandit, Arnab Saha
Integers divisible by a shifted prime in a given interval
Rebecca Abi Abdallah, Valeriya Kovaleva, Jeremy Schlitt et al.
On Piatetski-Shapiro primes from almost primes
Yuhua Zhao, Jinjiang Li, Linji Long et al.
On Consecutive Non-primitive Elements over Finite Fields
Bidushi Sharma, Dhiren Kumar Basnet
Birch's theorem over function fields with quadratically many variables
Matthew Hase-Liu