On the p^\lambda problem

@article{Baier2004OnTP,
  title={On the p^\lambda problem},
  author={S. Baier},
  journal={Acta Arithmetica},
  year={2004},
  volume={113},
  pages={77-101}
}
  • S. Baier
  • Published 2004
  • Mathematics
  • Acta Arithmetica
We deal with the distribution of the fractional parts of $p^{\lambda}$, $p$ running over the prime numbers and $\lambda$ being a fixed real number lying in the interval $(0,1)$. Roughly speaking, we study the following question: Given a real $\theta$, how small may $\delta>0$ be choosen if we suppose that the number of primes $p\le N$ satisfying ${p^{\lambda}-\theta<\delta}$ is close to the expected one? We improve some results of Balog and Harman on this question for $\lambda<5/66$ if $\theta… Expand
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References

SHOWING 1-5 OF 5 REFERENCES
REPRESENTATIONS OF PRIMES BY QUADRATIC FORMS.
  • 10
Gaussian primes in Narrow sectors
  • 20
  • PDF
On the distribution of v p modulo one
  • 47
  • Highly Influential
On mean values of Dirichlet polynomials
  • 4
  • Highly Influential
The Riemann zeta-function
  • 594