## Number Theory Seminar

- Event Type
- Seminar/Symposium
- Sponsor
- Department of Mathematics
- Location
- Literature, Cultures, and Linguistics Building, Room G-32
- Date
- Sep 26, 2023 11:00 - 11:50 am
- Speaker
- Kunjakanan Nath (UIUC)
- Contact
- Jesse Thorner and Yuan Liu
- jat9@illinois.edu and yyyliu@illinois.edu
- Views
- 27
- Originating Calendar
- Number Theory Seminar Calendar
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 $S(N)$.