We explicitly construct an extractor for two independent sources on
$n$ bits, each with min-entropy at least $\log^C n$ for a large
enough constant $C$. Our extractor outputs one bit and has error
$n^{-\Omega(1)}$. The best previous extractor, by...
We explicitly construct an extractor for two independent sources on
$n$ bits, each with min-entropy at least $\log^C n$ for a large
enough constant $C$. Our extractor outputs one bit and has error
$n^{-\Omega(1)}$. The best previous extractor, by...
Starting from the Poisson summation formula, I discuss spectral
summation formulae on GL(2) and GL(3) and present a variety of
applications to automorphic forms, analytic number theory, and
arithmetic.
The Bernoulli convolution with parameter $\lambda$ is the law of
the random variable: $\sum X_i \lambda^i$, where $X_i$ are
independent unbiased $+1/-1$ valued random variables. If $\lambda
1/2$, then the Bernoulli convolution is singular and is...
