Distribution of integers that are sums of three squares of primes
نویسندگان
چکیده
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.
متن کاملRepresenting Integers as Sums of Squares
We study in detail the special case of Waring’s problem when the power k = 2. Ultimately, we prove that four is the least number of squares needed to represent any integer. To this end, we prove that some numbers cannot be represented as sums of two squares, some cannot be represented as sums of three, and all can be represented as sums of four. We also show that numbers of a certain form can b...
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چکیده ندارد.
15 صفحه اولOn Sums of Three Squares
(1) r3(n) = 4πn S3(n), where the singular series S3(n) is given by (16) with Q = ∞. While in principle this exact formula can be used to answer almost any question concerning r3(n), the ensuing calculations can be tricky because of the slow convergence of the singular series S3(n). Thus, one often sidesteps (1) and attacks problems involving r3(n) directly. For example, concerning the mean valu...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2001
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa98-3-1