In a paper with the above title, T. M. Apostol and S. Chowla [1] proved the following result:
Theorem 1.For relatively prime integers h and k, l ≤ h ≤ k, the series
does not admit of an Euler product decomposition, that is, an identity of the form
1
except when h = k = l; fc = 1, fc = 2. The series on the right is extended over all primes p and is assumed to be absolutely convergent for
R(s)>1.