Among the bounty of brilliancies bequeathed to humanity by
Srinivasa Ramanujan, the circle method and the notion of mock theta
functions strike wonder and spark intrigue in number theorists
fresh and seasoned alike. The former creation was honed...
A well known result of Coleman says that p-adic overconvergent
(ellitpic) eigenforms of small slope are actually classical modular
forms. Now consider an overconvergent p-adic Hilbert eigenform F
for a totally real field L. When p is totally...
We define a polynomial threshold function to be a function of
the form f(x) = sgn(p(x)) for p a polynomial. We discuss some
recent techniques for dealing with polynomial threshold functions,
particular when evaluated on random Gaussians. We...
It is well-known that any Boolean function f:{-1,+1}^n \to
{-1,+1} can be written uniquely as a polynomial f(x) = \sum_{S
subset [n]} f_s \prod_{i in S} x_i. The collection of coefficients
(f_S's) this expression are referred to (with good reason)...
