There is not much here.

Here is link to my what I believe to be a correct proof that there an infinite number of twinned primes.
I used mathematical analysis techniques usually associated with signal processing, (the Fouries Series and Fourier transforms) and physics (Poisson resummation). The basic form of the proof is to use Fourier series to transform the sifting functions of a modified Sieve of Eratothenes from discrete integer functions into discontinuous, but real functions. This allows one to bring to bear the power of a real and complex analysis to the problem.

The bane of all such sieve approaches to prime number distributions, is to prove the variation about the asymptotic average has an acceptably small bound. With the use of the Poisson resummation, I am able to prove the error term is bounded by twice the number of strands in the sieve.

This bound turns out to be accepably small and suffices to prove there is at least prime number, P, in the range of 1 < P < P_r; where P_r is the r-th prime; i.e. P_1 = 2, P2 = 3, P_3 = 5, P_4 = 7, P_5 = 11, etc.

A side-effect of the Fourier series research, is I have run across the Fourier series of functions with interesting Fourier coefficients. Here is my current list of these Fourier series.

I have also had the occassion to generalize one of the Hilbert inequalities. The proof of the generalization is a simple consolidation of work by Jameson, Montgomery, and Davenport. The only thing original in the proof is extending the inequality to include rational coefficients in the denominator of the sum.

Here is a a paper I posted to he arXiv pre-print archive on the Auto and Cross Correlation of Ramanujan Sums. I am in the process of removing the paper from the archive as it has an error. The Bochner-Fejer kernels converge uniformily to the related almost periodic function only where the a.p. function is continuous. In my paper I fail to prove the Ramanujn-Fourier functions are continuous at the intervals of interest (e.g. intervals of non-zero measure centered on the integers)(

Since, I am exploring almost periodic function and their connection to Ramanujan expansions, I created this Map of Almost Periodic Function/Spaces for myself. I hope it helps you as well.