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arXiv · 1509.04378

Bounded Gaps Between Primes in Multidimensional Hecke Equidistribution Problems

Jesse Thorner
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Abstract

Using Duke's large sieve inequality for Hecke Gr{\"o}ssencharaktere and the new sieve methods of Maynard and Tao, we prove a general result on gaps between primes in the context of multidimensional Hecke equidistribution. As an application, for any fixed $0<\epsilon<\frac{1}{2}$, we prove the existence of infinitely many bounded gaps between primes of the form $p=a^2+b^2$ such that $|a|<\epsilon\sqrt{p}$. Furthermore, for certain diagonal curves $\mathcal{C}:ax^{\alpha}+by^{\beta}=c$, we obtain infinitely many bounded gaps between the primes $p$ such that $|p+1-\#\mathcal{C}(\mathbb{F}_p)|<\epsilon\sqrt{p}$.

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Jesse Thorner. 2015-09-15. Bounded Gaps Between Primes in Multidimensional Hecke Equidistribution Problems. https://doi.org/10.4310/mrl.2019.v26.n3.a9

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