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Sums of one prime power and two squares of primes in short intervals

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Let k≥1 be an integer. We prove that a suitable asymptotic formula for the average number of representations of integers n=p1k+p22+p32, where p1, p2, p3 are prime numbers, holds in… Click to show full abstract

Let k≥1 be an integer. We prove that a suitable asymptotic formula for the average number of representations of integers n=p1k+p22+p32, where p1, p2, p3 are prime numbers, holds in intervals shorter than the ones previously known.

Keywords: squares primes; prime power; sums one; two squares; power two; one prime

Journal Title: Rocky Mountain Journal of Mathematics
Year Published: 2021

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