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Journal Articles Mathematische Annalen Year : 2021

Lemke Oliver and Soundararajan bias for consecutive sums of two squares

Abstract

In a surprising recent work, Lemke Oliver and Soundararajan noticed how experimental data exhibits erratic distributions for consecutive pairs of primes in arithmetic progressions, and proposed a heuristic model based on the Hardy--Littlewood conjectures containing a large secondary term, which fits the data very well. In this paper, we study consecutive pairs of sums of squares in arithmetic progressions, and develop a similar heuristic model based on the Hardy--Littlewood conjecture for sums of squares, which also explain the biases in the experimental data. In the process, we prove several results related to averages of the Hardy--Littlewood constant in the context of sums of two squares.

Dates and versions

hal-03345856 , version 1 (15-09-2021)

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Chantal David, Lucile Devin, Jungbae Nam, Jeremy Schlitt. Lemke Oliver and Soundararajan bias for consecutive sums of two squares. Mathematische Annalen, In press, ⟨10.1007/s00208-021-02307-2⟩. ⟨hal-03345856⟩
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