Grant: Canada Research Chairs

The principal investigator is developing an alternative approach to analytic number theory, the first coherent program since Riemann's 1859 memoir. He can now reprove all classical results, quantitatively and qualitatively, providing simpler proofs of notoriously difficult results (E.g Theorems of Linnik and Hoheisel), and making advances that seemed inaccessible to classical methods. Now the principal investigator wishes to understand the existence of, and evaluate, mean values, find how to integrate triple products (to show there are primes in short intervals), find higher order cancelation, study higher weight L-functions, develop links to additive combinatorics and to the sieve, and exploit the dispersion method.