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Reveals an asymptotic formula for number partitions into sums of squares, suggesting new techniques for analysis.
In this paper, we use a variation of the Circle Method, along with the Saddle Point Method, to obtain an asymptotic formula for the number of partitions of a number [Formula: see text] into integers which are sums of two squares. Unlike previous work on partitions into restricted parts, we need to handle a Dirichlet series with a fractional singularity.
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Jaime Palacios (2026) studied this question.
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