James Maynard: On the theory of prime producing sieves, part 1 (NTWS 223)

Abstract: The closest thing to a general method for counting primes in a set is the method of Type I/II sums. This allows one to obtain an asymptotic formula (or perhaps a non-trivial lower bound) for the number of primes in the set, provided one has sufficiently good estimates for certain auxiliary sums.
Unfortunately what counts as 'sufficiently good' is poorly understood, as are the limits of this approach. In this talk, I'll discuss a new framework (joint with Kevin Ford) which allows us to prove necessary and sufficient conditions in various cases, focusing on general features and illustrating the method with some simple examples.
Link to slides: drive.google.c...
Number Theory Web Seminar: www.ntwebsemin...
Original air date:
Thursday, October 10, 2024 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, October 11, 2024 (2am AEDT, 4am NZDT)