Higher moments of primes in short intervals II
نویسنده
چکیده
Given good knowledge on the even moments, we derive asymptotic formulas for λ-th moments of primes in short intervals and prove “equivalence” result on odd moments. We also provide numerical evidence in support of these results.
منابع مشابه
Equivalence of higher moments of primes in short intervals
In this article, we prove an “equivalence” between two higher even moments of primes in short intervals under Riemann Hypothesis. We also provide numerical evidence in support of these asymptotic formulas.
متن کاملHigher moments of primes in short intervals I
In this article, we prove an “equivalence” between two higher even moments of primes in short intervals under Riemann Hypothesis. We also provide numerical evidence in support of these asymptotic formulas.
متن کاملλ-th moments of primes in short intervals
Given good knowledge on the even moments, we derive asymptotic formulas for λ-th moments of primes in short intervals and prove “equivalence” result on odd moments. We also provide numerical evidence in support of these results.
متن کاملMore precise pair correlation of zeros and primes in short intervals
Goldston and Montgomery [3] proved that the Strong Pair Correlation Conjecture and two second moments of primes in short intervals are equivalent to each other under Riemann Hypothesis. In this paper, we get the second main terms for each of the above and show that they are almost equivalent to each other.
متن کاملHigher Correlations of Divisor Sums Related to Primes Iii: Small Gaps between Primes
We use divisor sums to approximate prime tuples and moments for primes in short intervals. By connecting these results to classical moment problems we are able to prove that, for any η > 0, a positive proportion of consecutive primes are within 4 + η times the average spacing between primes. Authors’ note. This paper was written in 2004, prior to the solution, in [8], of the problem considered ...
متن کامل