Primes with restricted digits
成果类型：
Article
署名作者：
Maynard, James
署名单位：
University of Oxford
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-019-00865-6
发表日期：
2019
页码：
127-218
关键词：
摘要：
Let a0{0,...,9}. We show there are infinitely many prime numbers which do not have the digit a0 in their decimal expansion. The proof is an application of the Hardy-Littlewood circle method to a binary problem, and rests on obtaining suitable Type I' and Type II' arithmetic information for use in Harman's sieve to control the minor arcs. This is obtained by decorrelating Diophantine conditions which dictate when the Fourier transform of the primes is large from digital conditions which dictate when the Fourier transform of numbers with restricted digits is large. These estimates rely on a combination of the geometry of numbers, the large sieve and moment estimates obtained by comparison with a Markov process.
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