From a cotangent sum to a generalized totient function

Michael Rassias

doi:10.2298/aadm1702369m

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.

Highlights

B, n ∈ N, let na na na xn := b =−, b b where u stands for the floor function of the real number u
In this paper we investigate a certain category of cotangent sums and the sum b−1 cot πm sin3
One of the methods used consists in the exploitation of relations between trigonometric sums and the fractional part of a real number

Summary

FROM A COTANGENT SUM TO A GENERALIZED TOTIENT FUNCTION

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

INTRODUCTION

That is