Geodesic
Non-Abelian Generalizations of the Erdős-Kac Theorem
Canadian journal of mathematics, Tome 56 (2004) no. 2, pp. 356-372

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

Let $a$ be a natural number greater than 1. Let ${{f}_{a}}\left( n \right)$ be the order of $a\,\bmod \,n$ . Denote by $\omega \left( n \right)$ the number of distinct prime factors of $n$ . Assuming a weak form of the generalised Riemann hypothesis, we prove the following conjecture of Erdös and Pomerance: The number of $n\,\le \,x$ coprime to a satisfying $$\alpha \le \frac{\omega \left( {{f}_{a}}\left( n \right) \right)-{{\left( \log \,\log \,n \right)}^{2}}/2}{{{\left( \log \,\log \,n \right)}^{3/2}}/\sqrt{3}}\le \beta $$ is asymptotic to $\left( \frac{1}{\sqrt{2\pi }}\int_{\alpha }^{\beta }{{{e}^{-{{t}^{2}}/2}}}dt \right)\frac{x\phi \left( a \right)}{a}$ as $x$ tends to infinity.
DOI : 10.4153/CJM-2004-017-7
Mots-clés : 11K36, 11K99, Turán's theorem, Erdős-Kac theorem, Chebotarev density theorem, Erdős-Pomerance conjecture 
Murty, M. Ram; Saidak, Filip. Non-Abelian Generalizations of the Erdős-Kac Theorem. Canadian journal of mathematics, Tome 56 (2004) no. 2, pp. 356-372. doi: 10.4153/CJM-2004-017-7
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