February 13, 2024Open Access

Applications of multiplicative functions to arithmetic statistics and Diophantine equations

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Abstract

We prove matching upper and lower bounds for the average of the 6-torsion of class groups of quadratic fields. Furthermore, we count the number of integer solutions on an affine quartic surface. These, and other, applications follow from a result that we establish in this paper regarding the average of multiplicative functions over a general integer sequence.

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Chan et al. (Tue,) studied this question.

synapsesocial.com/papers/68e796c9b6db643587707709 https://doi.org/https://doi.org/10.48550/arxiv.2402.08710

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