Primes and polynomials with restricted digits

James Maynard

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arXiv · 1510.07711

Primes and polynomials with restricted digits

James Maynard

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Abstract

Let $q$ be a sufficiently large integer, and $a_0\in\{0,\dots,q-1\}$. We show there are infinitely many prime numbers which do not have the digit $a_0$ in their base $q$ expansion. Similar results are obtained for values of a polynomial (satisfying the necessary local conditions) and if multiple digits are excluded. Our proof is based on the Hardy-Littlewood circle method and Fourier analysis of the set of integers with no digit equal to $a_0$ in base $q$.

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BibTeX RIS

James Maynard. 2015-10-26. Primes and polynomials with restricted digits. https://arxiv.org/abs/1510.07711

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