On Jordan's generalization of Euler's function
Let \(\alpha\) be a natural number and \(\varphi_\alpha(n)\) the number of vectors \((m_1, m_2,\dots, m_\alpha)\) with \(1\leq m_1,\dots, m_\alpha\leq n\) and \(\operatorname {gcd} (m_1,\dots, m_\alpha,n)= 1\). The case \(\alpha=1\) is Euler's \(\varphi\)-function. The author proves identities between the Jordan totients \(\varphi_\alpha\) and greatest common divisors of numbers. He explains some of the identities on finite Heisenberg groups.
scientific article; zbMATH DE number 1383730
scientific article