Speaker: Kunjakanan Nath (UIUC)
Title: On binary problems in analytic number theory
Abstract: Given any two sequences ${a(n)}_{n=1}^\infty$ and ${b(n)}_{n=1}^\infty$ of ''number-theoretic'' interest, consider a binary problem of the form $S(N):=\sum_{n=1}^{N} a(n)b(n)$. In general, it is an extremely difficult question to evaluate the sum $S(N)$. In this talk, we will give a few examples to demonstrate the application of Fourier analysis in conjunction with the arithmetic structure of the given sequence and the bilinear form method to estimate the sum $S(N)$.
