University of Connecticut

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Algebra Seminar
How Often Is The Order Odd Modulo A Prime?
Jeremy Rouse (Wake Forest University)

Wednesday, February 24, 2021
11:15am – 12:05pm

Storrs Campus
Online on WebEx

If you choose a prime number \(p\) at random, what are the chances that it divides a number of the form \(2^{k} + 1\)? This question was answered by Hasse, and we will consider an elliptic curve analogue of this problem where we start with an elliptic curve \(E/\mathbb{Q}\), a point \(\alpha \in E(\mathbb{Q})\) with infinite order, and ask how often \(\overline{\alpha} \in E(\mathbb{F}_{p})\) has odd order. We show that this is related to the image of a certain Galois representation, study its image, and use this to determine how large and how small the density of primes \(p\) for which \(\alpha\) has odd order can be (under natural restrictions on \(\alpha\)).

Please contact the organizer for the WebEx link.


Algebra Seminar (primary), College of Liberal Arts and Sciences, UConn Master Calendar

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