Abstract
We mentioned in Chapter 1 that the number r s (n) of solutions of the Diophantine equation
is the coefficient of xn in the Taylor expansion of the function \( 1 + \sum\nolimits_{{n = 1}}^{\infty } {{r_s}(n){x^n}} \). Here, as in Chapter 8, we write θ(x) for θ3(1;x) and we shall suppress the first entry, which will always be z = 1. From (12.1); it follows, by Cauchy’s theorem, that
where, we recall,
and 𝓒 is a sufficiently small circle around the origin.
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© 1985 Springer-Verlag New York Inc.
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Grosswald, E. (1985). The Circle Method. In: Representations of Integers as Sums of Squares. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8566-0_13
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DOI: https://doi.org/10.1007/978-1-4613-8566-0_13
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