Limit Theorems for Empirical Density of Greatest Common Divisors
2016 ◽
Vol 161
(3)
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pp. 517-533
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AbstractThe law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. We study the large deviations of the empirical density. We will also obtain a rate of convergence to the normal distribution for the central limit theorem. Some generalisations are provided.
2017 ◽
Vol 54
(2)
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pp. 569-587
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2018 ◽
Vol 61
(2)
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pp. 363-369
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1999 ◽
Vol 96
(5)
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pp. 3455-3471
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1969 ◽
Vol 136
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pp. 545
Keyword(s):
2008 ◽
Vol 11
(02)
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pp. 213-229
Keyword(s):
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1990 ◽
Vol 65
(12)
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pp. 1391-1394
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