# Monthly Archives: February 2012

## Symmetrization

We call a random variable (which is just a measurable function where is a probability measure space) symmetric if is identically distributed to . Symmetric random variables are often a lot more pleasant to handle. Much of what is true … Continue reading

## Every large number is the sum of 13 cubes

An important function that arises from Waring’s problem is the the following. For any , let be the least such that, for all sufficiently large (how large can depend on and ) there exist positive integers such that Waring’s problem … Continue reading

## Hardy and the zeta function, Part 1

Today we’ll begin with an interesting and important theorem about the Riemann zeta function. Recall that this is defined when by the absolutely convergent series This can be analytically continued to a function meromorphic on the entire complex plane, holomorphic … Continue reading