Profile directory About Mobile apps
Log in Sign up
arXiv Math @arxiv_math@qoto.org
Follow

Improvements on exponential sums related to Piatetski-Shapiro primes https://arxiv.org/abs/2504.11464 #mathNT

Improvements on exponential sums related to Piatetski-Shapiro primes

We prove a new bound to the exponential sum of the form $$ \sum_{h \sim H}δ_h \mathop{\sum_{m\sim M}\sum_{n\sim N}}_{mn\sim x}a_{m}b_{n}\e\big(αmn + h(mn + u)^γ\big), $$ 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 $\lfloor n^c \rfloor$. 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 the intersection of multiple Beatty sequences and so on.

arXiv.org
April 18, 2025 at 3:10 AM · · feed2toot · 0 · 0 · 0
Sign in to participate in the conversation
Qoto Mastodon

QOTO: Question Others to Teach Ourselves
An inclusive, Academic Freedom, instance
All cultures welcome.
Hate speech and harassment strictly forbidden.

Trending now

#rebrandwebsitesortech0 people talking
0
#HashtagGames0 people talking
0

Resources

  • Terms of service
  • Privacy policy

Developers

  • Documentation
  • API

What is Mastodon?

qoto.org

  • About
  • v3.5.19-qoto

More…

  • Source code
  • Mobile apps
v3.5.19-qoto · Privacy policy