166 citations · 562 across the 54 of their papers we have counts for
12 papers · 1 filter
Correlation of arithmetic functions over
Ofir Gorodetsky, Will Sawin
For a fixed polynomial , we study the number of polynomials of degree over such that and are both irreducible, an -analogue of th…
Free rational curves on low degree hypersurfaces and the circle method
Tim Browning, Will Sawin
We use a function field version of the Hardy-Littlewood circle method to study the locus of free rational curves on an arbitrary smooth projective hypersurface of sufficiently low…
Chebotarev density theorem in short intervals for extensions of
Lior Bary-Soroker, Ofir Gorodetsky, Taelin Karidi +1
An old open problem in number theory is whether Chebotarev density theorem holds in short intervals. More precisely, given a Galois extension of with Galois group…
A representation theory approach to integral moments of L-functions over function fields
Will Sawin
We propose a new heuristic approach to integral moments of L-functions over function fields, which we demonstrate in the case of Dirichlet characters ramified at one place (the fun…
Dynamical models for Liouville and obstructions to further progress on sign patterns
Will Sawin
We define a class of dynamical systems by modifying a construction due to Tao, which includes certain Furstenburg limits arising from the Liouville function. Most recent progress o…
Square-root cancellation for sums of factorization functions over short intervals in function fields
Will Sawin
We present new estimates for sums of the divisor function, and other similar arithmetic functions, in short intervals over function fields. (When the intervals are long, one obtain…
On the Ramanujan conjecture for automorphic forms over function fields I. Geometry
Will Sawin, Nicolas Templier
Let be a split semisimple group over a function field. We prove the temperedness at unramified places of automorphic representations of , subject to a local assumption at on…
The equidistribution of L-functions of twists by Witt vector Dirichlet characters over function fields
Will Sawin
Katz showed that the L-functions of all Dirichlet characters of F_q(t), with conductor a fixed power of a degree one prime, are equidistributed in the limit as q goes to infinity.…
The second moment theory of families of L-functions
Valentin Blomer, Étienne Fouvry, Emmanuel Kowalski +3
For a fairly general family of L-functions, we survey the known consequences of the existence of asymptotic formulas with power-sawing error term for the (twisted) first and second…
Irreducibility of polynomials with a large gap
William Sawin, Mark Shusterman, Michael Stoll
We generalize an approach from a 1960 paper by Ljunggren, leading to a practical algorithm that determines the set of such that…
Monodromy of elliptic curve convolution, seven-point sheaves of -type and motives of Beauville type
Benjamin Collas, Michael Dettweiler, Stefan Reiter +1
We study the Tannakian properties of the category of perverse sheaves on elliptic curves endowed with the convolution product. We establish that for certain sheaves with unipotent…
Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums
E. Kowalski, Ph. Michel, W. Sawin
We prove non-trivial bounds for bilinear forms with hyper-Kloosterman sums with characters modulo a prime which, for both variables of length , are non-trivial as soon as $M…