Higher Correlations of Divisor Sums Related to Primes I: Triple Correlations
نویسندگان
چکیده
We obtain the triple correlations for a truncated divisor sum related to primes. We also obtain the mixed correlations for this divisor sum when it is summed over the primes, and give some applications to primes in short intervals.
منابع مشابه
HIGHER CORRELATIONS OF DIVISOR SUMS RELATED TO PRIMES III: k-CORRELATIONS
We obtain the general k-correlations for a short divisor sum related to primes.
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We calculate the triple correlations for the truncated divisor sum λR(n). The λR(n) behave over certain averages just as the prime counting von Mangoldt function Λ(n) does or is conjectured to do. We also calculate the mixed (with a factor of Λ(n)) correlations. The results for the moments up to the third degree, and therefore the implications for the distribution of primes in short intervals, ...
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Abstract. We calculate the triple correlations for the truncated divisor sum λR(n). The λR(n)’s behave over certain averages just as the prime counting von Mangoldt function Λ(n) does or is conjectured to do. We also calculate the mixed (with a factor of Λ(n)) correlations. The results for the moments up to the third degree, and therefore the implications for the distribution of primes in short...
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