Zeta types and tannakian symbols as a method for representing mathematical knowledge

Abstract

We present two closely related notions called (1) a zeta type and (2) a Tannakian symbol. These are data types for representing information about number-theoretic objects, and we argue that a database built out of zeta types and Tannakian symbols could lead to interesting discoveries, similar to what has been achieved for example by the OEIS, the LMFDB, and other existing databases of mathematical objects. We give several examples illustrating what database records would look like, and we describe a tiny prototype database which has already been used to find and automatically prove new theorems about multiplicative functions.