Generalized Dedekind ψ-functions with respect to a polynomial. II

J. Chidambaraswamy

Vol. 65 (1976), No. 1, 19–27

DOI: 10.2140/pjm.1976.65.19

Abstract

For a given polynomial f = f(x) of positive degree with integer coefficients and for given positive integers u, v, and t, the arithmetical function ψ_f,t^u,v(n) is defined and some of its arithmetical properties are obtained in addition to its average order. ψ_x,1^k,1(n) reduces to the function ψ_(k)(n) studied recently by D. Suryanarayana and ψ_f,t^1,k(n) to ψ_f,t^(k)(n) studied more recently by the author.

Mathematical Subject Classification

Primary: 10A20, 10A20

Secondary: 10H25

Milestones

Received: 17 April 1975

Revised: 27 January 1976

Published: 1 July 1976