Bibliographic Details
| Title: |
Improvements on exponential sums related to Piatetski-Shapiro primes. |
| Authors: |
Lu, Li1 (AUTHOR) lilu_math@foxmail.com, Guo, Lingyu1 (AUTHOR) guo.lingyu@foxmail.com, Guo, Victor Zhenyu1 (AUTHOR) guozyv@xjtu.edu.cn |
| Source: |
Journal of Number Theory. Apr2026, Vol. 281, p700-725. 26p. |
| Subjects: |
Exponential sums, Prime numbers, Number theory |
| Abstract: |
We prove a new bound to the exponential sum of the form ∑ h ∼ H δ h ∑ m ∼ M ∑ n ∼ N m n ∼ x a m b n e (α m n + h (m n + u) γ) , by a new approach to the Type I sum. The sum can be applied to many problems related to Piatetski-Shapiro primes, which are primes of the form ⌊ n c ⌋. In this paper, we improve the admissible range of the Balog-Friedlander condition, which leads to an improvement to the ternary Goldbach problem with Piatetski-Shapiro primes. We also investigate the distribution of Piatetski-Shapiro primes in arithmetic progressions, Piatetski-Shapiro primes in a Beatty sequence and so on. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
