Large Deviation Results and Applications to the Generalized Cramér Model

Large Deviation Results and Applications to the Generalized Cramér Model

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) s...

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Veröffentlicht in:Mathematics (Basel) 2018-04, Vol.6 (4), p.49
Hauptverfasser: Giuliano, Rita, Macci, Claudio
Format: Artikel
Sprache:eng
Schlagworte:
Arithmetic
arithmetic progressions
Deviation
first Chebyshev function
Number theory
Numbers
products of primes
Progressions
Random variables
regularly varying functions
slowly varying functions
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Zusammenfassung: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math6040049