Prime structures in sums of two squaresMPIM

by Cihan Sabuncu (MPIM)

Wednesday Oct 8, 2025, 2:30 PM → 3:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Number theory lunch seminar

The problem of representing numbers as sums of two squares has a long and rich history, connecting arithmetic with geometry and producing a sequence with remarkable structure. For instance, the classical representation function for sums of two squares is (more-or-less) multiplicative.

In this talk, we shift focus to two related but more delicate functions: the representation function for sums of two prime squares, and the representation function for sums of a square and a prime square. We will examine the statistical behaviour of these representation functions, with particular attention to the moments of the former and the distribution of the latter.

Part of this talk is based on joint work with Andrew Granville and Alisa Sedunova.