This research investigates variance in sums of perfect squares, suggesting connections to L-functions and the Riemann hypothesis.
Let if is the sum of two perfect squares, and otherwise. We study the variance of in short intervals by relating the variance with the second moment of the generating function along . We develop a new method for estimating fractional moments of ‐functions and apply it to the second moment of to bound the variance of . Our results are conditional on the Riemann hypothesis for the zeta‐function and the Dirichlet ‐function associated with the non‐principal character modulo 4.
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Baluyot et al. (2025) studied this question.
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