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Mathematics 2018, 6(4), 49; https://doi.org/10.3390/math6040049

Large Deviation Results and Applications to the Generalized Cramér Model

1
Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy
2
Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, I-00133 Rome, Italy
*
Author to whom correspondence should be addressed.
The support of INdAM (Fondi GNAMPA) and Università di Pisa (Fondi di Ateneo) is acknowledged. The first version of this paper was written during the staying of the first author at the University Jean Monnet (St. Etienne).
Received: 2 March 2018 / Revised: 25 March 2018 / Accepted: 27 March 2018 / Published: 2 April 2018
(This article belongs to the Special Issue Stochastic Processes with Applications)
Full-Text   |   PDF [301 KB, uploaded 3 May 2018]

Abstract

In this paper, we prove large deviation results for some sequences of weighted sums of random variables. These sequences have applications to the probabilistic generalized Cramér model for products of primes in arithmetic progressions; they could lead to new conjectures concerning the (non-random) set of products of primes in arithmetic progressions, a relevant topic in number theory. View Full-Text
Keywords: arithmetic progressions; first Chebyshev function; products of primes; regularly varying functions; slowly varying functions arithmetic progressions; first Chebyshev function; products of primes; regularly varying functions; slowly varying functions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Giuliano, R.; Macci, C. Large Deviation Results and Applications to the Generalized Cramér Model
. Mathematics 2018, 6, 49.

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