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Friday, February 12, 2016
4:00 PM - 5:00 PM

Number Theory Seminar

Primes with restricted digits
James Maynard, Professor, Mathematical Institute, Magdalen College University of Oxford,

Many important questions ask for showing the existence of primes in `thin' sets  - those with $O(x^{1-\epsilon})$ elements less than $x$. The thinness of such sets presents several analytic difficulties.

 

The set of numbers with the digit 7 not appearing anywhere in their decimal expansion is a thin set, but has some unusually nice properties which circumvents some (but not all) of these analytic difficulties, and so is a nice test case. We show that there are infinitely many primes in this set. Our proof uses a mixture of bilinear sums, Fourier analysis, geometry of numbers and moment estimates related to a Markov process.

For more information, please contact Elena Mantovan by email at mathinfo@caltech.edu or visit http://math.caltech.edu/~numbertheory/.