DISCUSSION MEETING
L-FUNCTIONS, CIRCLE-METHOD AND APPLICATIONS (HYBRID)
ORGANIZERS: Soumya Das (IISc, Bengaluru, India), Ritabrata Munshi (ISI-Kolkata, India) and Saurabh Kumar Singh (IIT - Kanpur, India)
DATE: 27 June 2022 to 01 July 2022
VENUE: Ramanujan Lecture Hall and Online
The circle method originated in a paper of S. Ramanujan and G. H. Hardy on the partition function. This method has evolved with time and has seen many interesting applications. The classical applications of the circle method are to the Waring’s problem, to the ternary Gold-bach problem, and to count rational points on varieties. The modern applications of this method are to the subconvexity problem on various L-functions and to the shifted convolution problem. Also, the circle method is a powerful analytical tool to study correlations between two arithmetical functions and it is very flexible to use. The analytic study of L-functions is a central theme in analytic number theory, and it has many arithmetical consequences. The growth of L-functions (few classes of L-functions) can be understood by studying a correlation problem using the circle method. We hope that this method will continue to have many more interesting applications. The aim of this programe is to explore this method and look into its future.
CONTACT US: circlemthd@icts.res.in
PROGRAM LINK: [ Ссылка ]
Table of Contents (powered by [ Ссылка ])
0:00:00 Start
0:00:15 Zeros of the Derivatives of L Functions by Sneha Chaubey
0:07:48 Distribution of zeros of 3 (k) (s)
0:11:23 Remark
0:12:27 Another result of Distribution of zeros of KTH derivative
0:15:37 Yildirim
0:17:25 Selboy class
0:19:35 Theorem 1
0:25:37 Finiteness of zeros in the left half plane
0:26:03 Theorem 2
0:29:54 Sketch of proof - Theorem 2
0:36:16 Wrap Up
