Non-commutative q-expansions

TL;DR

This paper constructs a non-commutative q-expansion with coefficients in a non-commutative Iwasawa algebra, addressing a question about non-commutative p-adic zeta functions posed by Fukaya and Kato.

Contribution

It introduces a novel construction of q-expansions with non-commutative coefficients, advancing understanding of non-commutative p-adic zeta functions.

Findings

Constructed a q-expansion with non-commutative coefficients

Connected the constant term to a non-commutative p-adic zeta function

Partially answered Fukaya and Kato's question

Abstract

In this short note we partially answer a question of Fukaya and Kato by constructing a $q$-expansion with coefficients in a non-commutative Iwasawa algebra whose constant term is a non-commutative p-adic zeta function.