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On the Non-Existence of Certain Euler Products
Published online by Cambridge University Press: 20 November 2018
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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 forR(s)>1.
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- Copyright © Canadian Mathematical Society 1980