# Joshua Zelinsky

### Education

BA Yale 2007

PhD Boston University 2014

**Research:**

My research has been on three main topics: integer complexity, Artin representations and odd perfect numbers. More broadly, my research has focused on combinatorial aspects of analytic and algebraic number theory.

**Publications:** On the total number of prime factors of an odd perfect number (Accepted to Integers)

Upper bounds on the second largest prime factor of an odd perfect number (International Journal of Number Theory, 2019)

An improvement of an inequality of Ochem and Rao concerning odd perfect numbers (Integers, 2018)

Upper Bounds for the Number of Primitive Ray Class Characters With Conductor Below a Given Bound (Acta Arithmetica, 2016)- Note that the published version has tighter results than this preprint form.

Numbers with Integer Complexity Close to the Lower Bound (Integers, 2012)

Tau Numbers: A Partial Proof of a Conjecture and Other Results (Journal of Integer Sequences, 2002)

**Other items:**

Here is a very short (4 minutes) talk on some of my research on integer complexity. This video is intended for a general audience.

Here is a 20 minute, slightly more technical version of that material which was a pre-recorded talk for the Connecticut Summer School in Number Theory

**Teaching:** I currently teach at the Hopkins School in New Haven, CT. This year I'm teaching pre-calculus. I'm also teaching the senior seminar which is focusing on number theory.