Department of Mathematics - Master Calendar

View Full Calendar

Number Theory Seminar

Event Type
Seminar/Symposium
Sponsor
Department of Mathematics
Location
Mumford Hall 316N
Date
Oct 24, 2024   11:00 - 11:50 am  
Speaker
Robert Lemke Oliver (Tufts)
Contact
Jesse Thorner and Yuan Liu
E-Mail
jat9@illinois.edu and yyyliu@illinois.edu
Views
24
Originating Calendar
Number Theory Seminar Calendar

Title: The least prime whose Frobenius is in a rational equivalence class

Abstract: The Chebotarev density theorem is a powerful tool in number theory, in part because it guarantees the existence of primes whose Frobenius lies in a given conjugacy class in a fixed Galois extension of number fields.  However, for some applications, it is necessary to know not just that such primes exist, but to additionally know something about their size, say in terms of the degree and discriminant of the extension.  In this talk, I'll discuss forthcoming work with Cho and Zaman on the least prime with a specified Frobenius in a fixed Galois S_n extension.  Our approach is comparatively elementary, but when combined with existing results based on the zeros of L-functions, it leads to the strongest known bounds in this setting.

link for robots only