# Spectral action on noncommutative torus

## TL;DR

This paper computes the spectral action on the noncommutative torus using a Chamseddine--Connes formula, emphasizing the role of Diophantine conditions and establishing holomorphic continuation results for related series.

## Contribution

It introduces a method to evaluate the spectral action on noncommutative tori through zeta function computations, highlighting the significance of Diophantine conditions.

## Key findings

- Spectral action explicitly computed for noncommutative torus
- Holomorphic continuation of series established
- Diophantine condition's importance demonstrated

## Abstract

The spectral action on noncommutative torus is obtained, using a Chamseddine--Connes formula via computations of zeta functions. The importance of a Diophantine condition is outlined. Several results on holomorphic continuation of series of holomorphic functions are obtained in this context.