From a cotangent sum to a generalized totient function

Abstract

In this paper we investigate a certain category of cotangent sums and more specifically the sum ?b-1m=1 cot (?m/b) sin3 (2?m a/b) and associate the distribution of its values to a generalized totient function ?(n,A,B), where ?(n,A,B) := ? A?k?B(n,k)=1 1. One of the methods used consists in the exploitation of relations between trigonometric sums and the fractional part of a real number.

Locations

• arXiv (Cornell University) - View - PDF
• Applicable Analysis and Discrete Mathematics - View - PDF