HIGHER MOMENTS OF PRIMES IN SHORT INTERVALS II
نویسندگان
چکیده
منابع مشابه
Higher moments of primes in short intervals II
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 کاملEquivalence 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 کاملPrimes in Short Intervals
Contrary to what would be predicted on the basis of Cramér’s model concerning the distribution of prime numbers, we develop evidence that the distribution of ψ(x + H) − ψ(x), for 0 ≤ x ≤ N , is approximately normal with mean ∼ H and variance ∼ H logN/H , when N ≤ H ≤ N1−δ .
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2005
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042105000169