Sums of one prime power and two squares of primes in short intervals
نویسندگان
چکیده
Let k≥1 be an integer. We prove that a suitable asymptotic formula for the average number of representations integers n=p1k+p22+p32, where p1, p2, p3 are prime numbers, holds in intervals shorter than ones previously known.
منابع مشابه
Sums of Primes and Squares of Primes in Short Intervals
Let H2 denote the set of even integers n 6≡ 1 (mod 3). We prove that when H ≥ X, almost all integers n ∈ H2 ∩ (X,X + H] can be represented as the sum of a prime and the square of a prime. We also prove a similar result for sums of three squares of primes.
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چکیده ندارد.
15 صفحه اولSums of Two Squares in Short Intervals in Polynomial Rings over Finite Fields
Landau’s theorem asserts that the asymptotic density of sums of two squares in the interval 1 ≤ n ≤ x is K/ √ log x, where K is the Landau-Ramanujan constant. It is an old problem in number theory whether the asymptotic density remains the same in intervals |n− x| ≤ x for a fixed and x→∞. This work resolves a function field analogue of this problem, in the limit of a large finite field. More pr...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2021
ISSN: ['0035-7596', '1945-3795']
DOI: https://doi.org/10.1216/rmj.2021.51.213