142 citations · 752 across the 110 of their papers we have counts for
5 papers · 1 filter
Small Designs for Path Connected Spaces and Path Connected Homogeneous Spaces
Daniel M. Kane
We prove the existence of designs of small size in a number of contexts. In particular our techniques can be applied to prove the existence of -designs on of size $O_d(n…
A Small PRG for Polynomial Threshold Functions of Gaussians
Daniel M. Kane
We develop a pseudo-random generator to fool degree- polynomial threshold functions with respect to the Gaussian distribution. For any constant, we construct a pseudo-rand…
On the Number of ABC Solutions with Restricted Radical Sizes
Daniel M. Kane
We consider a variant of the ABC Conjecture, attempting to count the number of solutions to , in relatively prime integers each of absolute value less than wit…
Minimal S-universality criteria may vary in size
Noam D. Elkies, Daniel M. Kane, Scott D. Kominers
In this note, we give simple examples of sets S of quadratic forms that have minimal S-universality criteria of multiple cardinalities. This answers a question of Kim, Kim, and Oh…
Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions
Daniel M. Kane, Scott D. Kominers
For relatively prime positive integers and , we consider the least common multiple of the finite arithmetic progression $\{u_k:=u_…