The notion of a multiplicative function is one of the central building blocks of modern number theory, and were studied by Euler, Gauss and Ramanujan among others. Classical multiplicative functions work as machines giving key information about various properties of positive integers. For example, there is a function which outputs 1 if the input is a square number, and 0 otherwise. We study a specific class of multiplicative functions related to the famous Riemann zeta function, and find new algebraic structure and symmetries on these functions, which greatly simplifies and generalises many deep relations that number theorists had proven before us. To arrive at our results, we use many advanced tools of modern mathematics, including lambda-rings and category theory.

Scientific field

Mathematics

Country

Norway

Contestants

Torstein Vik
Ane Kristine Espeseth