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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Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • Paul T. Bateman
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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