# metadata.dc.description[].value
Preprint enviat per a la seva publicació en una revista científica: Manuscripta Math 57, 469–475 (1987). [https://doi.org/10.1007/BF01168672]

# metadata.dc.description.abstract[].value
The singular series has great importance in the study of the number of representations of a rational integer as a sum oí integral squares (cf. (3)).
As is known (cf. (3), [81) the sum of the singular series is jusi the average number
r(n, gen Jk) of representations of a positive integer n by the genus of the identity quadralic
form in k variables.
Bateman [2) calculated the sum of the singular series in the cases k = 3.4, following
Hardy and Hecke methocl~. His results can though more easily be obtained by using Siegel's
formula for the evaluation of r(n, gen lk).
In this paper we derive in sorne special cases a formula for r(n, gen lk)• from Siegel's
formula. which covers those considered by Bateman. We use Gauss-Weber sums to evaluate the
2-adic densities, which, in Siegel's rnethod, causes the main difficulties.
Our considerations in the case k • 24 also yield the celebrated Ramanujan's formula
about the number of representations of an integer as sum of 24 squares.
I wish to thank Professor P. Bayer for her encouragement in doing this paper.

# metadata.dc.relation.isformatof[].value
Reproducció digital del document original en paper [CRAI Biblioteca de Matemàtiques i Informàtica - Dipòsit Departament CAIXA 31.33]

# metadata.dc.source[].value
Preprints de Matemàtiques - Mathematics Preprint Series

# metadata.dc.subject.other[].value
Universitat de Barcelona. Institut de Matemàtica