# The asymptotic formula for the number of representations of an integer as a sum of five squares

• Paul T. Bateman
Part of the Progress in Mathematics book series (PM, volume 138)

## Abstract

In this paper we remark that the asymptotic formula for the number of representations of an integer as a sum of five squares can be derived by a simple elementary argument from Jacobi’s formula for the number of representations of an integer as a sum of four squares. A by-product of our argument is an asymptotic formula for the sum
$$\sum\limits_{|j| < n^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } {\sigma (n\, - \,j^2 ),}$$
Where σ denotes the sum-of-divisors function.

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