Consecutive sums of two squares in arithmetic progressions
Vivian Kuperberg (ETH Zürich)
Abstract: There are infinitely many primes whose last digit is $1$ such that the next prime also ends in a $1$, and in fact these primes have positive density in the set of all primes. However, it is an open problem to show that there are infinitely many primes ending in $1$ such that the next prime ends in $3$. In this talk, we'll instead consider the sequence of sums of two squares in increasing order. We'll show that there are infinitely many sums of two squares ending in $1$ such that the next sum of two squares ends in $3$, and in fact that these sums of two squares have positive density in the set of all sums of two squares. Joint work with Noam Kimmel.
algebraic geometrynumber theory
Audience: researchers in the topic
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