Algebraic functions with Fermat property, eigenvalues of transfer operator and Riemann zeros, and other open problems

TL;DR

This paper presents a collection of open problems across number theory, combinatorics, and representation theory, including connections between Riemann zeros and transfer operators, and properties of algebraic functions.

Contribution

It compiles and discusses several open problems, highlighting potential research directions and unexplored connections in various mathematical fields.

Findings

List of open problems in multiple mathematical disciplines

Connections suggested between Riemann zeros and transfer operator eigenvalues

Identification of unexplored properties of algebraic functions and sequences

Abstract

In this note we list a number of open problems in the fields of number theory, combinatorics, and representation theory: algebraic functions with Fermat property; power product expansion of the generating function for the partition function; relation between the non-trivial Riemann zeros and eigenvalues of the transfer operator; functional equation related to norm forms; two problems from geometric combinatorics; a problem on the moments of the Minkowski question mark function; a question in representation theory; a problem on interpolating the moments of the Stern's diatomic sequence; an arithmetic properties of the binary composition function.