Counting low degree number fields with almost prescribed successive minima
Counting low degree number fields with almost prescribed successive minima
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Sameera Vemulapalli, Princeton University
Meeting ID:听 920 2195 5230
Passcode:听 听 The three-digit integer that is the cube of the sum of its digits.听
The successive minima of an order in a degree n number field are n real numbers encoding information about the Euclidean structure of the order. How many orders in degree n number fields are there with almost prescribed successive minima, fixed Galois group, and bounded discriminant? In this talk, I will address this question for n = 3,4,5. The answers, appropriately interpreted, turn out to be piecewise linear functions on certain convex bodies. If time permits, I will also discuss function field analogs of this problem.