Primes and polynomials with restricted digits
Abstract
Let q be a sufficiently large integer, and a0∈\0,…,q-1\. We show there are infinitely many prime numbers which do not have the digit a0 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 a0 in base q.
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