Representation of Certain Logarithmic Functions as Polynomials with a Small Number of Nonzero Coefficients

摘要

We study an element of the ring of algebraic integers having the special form 1 - zλ. We obtain a formula for calculating its logarithmic functions. Thus, we verify the conjecture that logarithmic functions of the element 1 - zλ are polynomials in z such that z appears only in powers that are divisors of the number of the logarithmic function.