Presented by: Alexander Dunn, University of Illinois

The problem of determining partition asymptotics has a rich history dating back to Hardy and Ramanujan in the early 20th century. In 2015 Vaughn obtained asymptotic formulas for the number of partitions of an integer into squares.  Gafni extended this to $d$th powers. Here we obtain such formulas for the number of partitions into values of an arbitrary integer polynomial $f$ subject to some mild hypotheses. Our methods use an interplay of the circle method, the polylogarithm, and the Matsumoto-Weng zeta function. This is a joint work with Nicolas Robles.

Talk based on the preprint: https://arxiv.org/abs/1705.00384

About Pure mathematics seminars

We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.

Seminars are held on Tuesdays from 3pm to 3.50pm in Room 67-442 of the Priestley Building (Building 67).

Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.

Information for speakers

Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.

Room 67-442 has a data projector and a whiteboard.

If you wish to use the data projector, contact us a few days in advance of your talk to avoid technical delays on the day - there's a tight turnaround with room bookings.

Contact us

To arrange to use the projector, contact Benjamin Burton.

To volunteer to talk or to suggest a speaker, email Clement Maria or Huy Nguyen.

Venue

Priestley Building (67)
Room: 
442