Applications of Delta Method in Number Theory - Lecture 1

Explore a comprehensive lecture on the Applications of Delta Method in number theory, presented by Keshav Aggarwal at the International Centre for Theoretical Sciences. Part of a broader workshop on Circle Method and Related Topics, this 80-minute session serves as the first lecture in a series designed for advanced graduate students and post-doctoral researchers. Delve into the analytical techniques of number theory, specifically focusing on the delta method and its applications within the context of the circle method. The lecture is part of a two-week program featuring expert presentations on various forms of the circle method, their modern applications in L-functions, ergodic theory, and the Langlands program. Gain insights into this powerful analytic tool that has been instrumental in studying partition functions, the Waring problem, and counting rational points on varieties, while exploring its recent extensions to function fields and general number fields.