Waring-Goldbach Problem with Piatetski-Shapiro Primes
Yildirim Akbal, Ahmet Muhtar Guloglu
TL;DR
This paper establishes an asymptotic formula for representing large integers as sums of fixed powers of Piatetski-Shapiro primes, advancing the understanding of Waring-Goldbach problems with sparse prime sequences.
Contribution
It introduces a new variant of the Waring-Goldbach problem involving Piatetski-Shapiro primes and derives an asymptotic formula for the number of such representations.
Findings
Asymptotic formula for representations of large integers as sums of Piatetski-Shapiro primes.
Extension of Waring-Goldbach problem to sparse prime sequences.
New insights into the distribution of Piatetski-Shapiro primes.
Abstract
In this paper, we exhibit an asymptotic formula for the number of representations of a large integer as a sum of a fixed power of Piatetski-Shapiro primes, thereby establishing a variant of Waring-Goldbach problem with primes from a sparse sequence.
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