Geodesic
On the Non-Existence of Certain Euler Products
Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 371-372

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Subbarao, M. V. On the Non-Existence of Certain Euler Products. Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 371-372. doi: 10.4153/CMB-1980-054-7
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[1] 1. Apostol, T.M. and Chowla, S., On the Non-Existence of Certain Euler Products, Det Kongelige Norske Videnskabers Selskab Forhandlinger Vol. 32 (1959), No. II, 65-67. Google Scholar

[2] 2. James, R.D. and Ivan, Niven, Unique Factorization in Multiplicative Systems, Proc. Amer. Math. Soc. 5 (1954); 834-838, MR16 336. Google Scholar

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