2 papers
math.NT2023
Normal distribution of bad reduction
Robert J. Lemke Oliver, Daniel Loughran, Ari Shnidman
We prove normal distribution laws for primes of bad semistable reduction in families of curves. As a consequence, we deduce that when ordered by height, of curves in these…
math.NT2017
The distribution of consecutive prime biases and sums of sawtooth random variables
Robert J. Lemke Oliver, Kannan Soundararajan
In recent work, we considered the frequencies of patterns of consecutive primes and numerically found biases toward certain patterns and against others. We made a conjec…