Josh Males

About Image


In October 2017 I joined Prof. Dr. Kathrin Bringmann's group at the University of Cologne, Germany. Prior to this I completed my masters at Durham University, UK under the supervision of Dr. Jens Funke .

I am interested in all areas of analytic and algebraic number theory, but my work currently focuses on quantum modular forms (of higher depth) and their properties.

Please note that this site is a work in progress. In particular the smooth scroll is having issues with Chrome, which I will try to fix soon


Below is a collection of papers, along with some of my own brief notes that are not intended to be published


  • Explicit modularity properties for exotic Bailey-Slater SPT functions - in preparation
  • Asymptotic equidistribution and a convexity result for Dyson's partition ranks (2019) - submitted, preprint available here
  • A family of vector-valued quantum modular forms of depth two (2018) - submitted, preprint available here


  • A short note computing higher Mordell integrals associated to higher depth quantum modular forms (2018) - pdf here
  • Masters Thesis - Topics in Modular Forms (2016) - pdf here

Referee work


  • Algebraic Number Theory, SS 2019 (with Dr. Stephan Ehlen)
  • Seminar on L-Functions , SS 2019 (with Prof. Bringmann)
  • Seminar on Theta Functions, WS 2018 (with Prof. Bringmann)


Below is a list of students who I co-supervise(d).

Master Students
  • Robin Sauer, 'Modular Forms Associated to Real Quadratic Fields', 2018
Bachelor Students
  • Julian Sander, 'Jensen Formula for Modular Functions', 2019 - present
  • Carsten Mitzkus, 'Fourier Coefficients of a Certain Eta-Quotient', 2017-18


My office hours are on Tuesdays 10-11.30am, Thursdays 2:30-4pm, or by arrangement. Please email me at if you need a different time.




Mathematical Institute

University of Cologne

Gyrhofstr. 8b

50931 Cologne