# 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} }

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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