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DC Field | Value | Language |
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dc.contributor.author | Arenas, A. (Àngela), 1955- | - |
dc.date.accessioned | 2020-03-02T12:52:15Z | - |
dc.date.available | 2020-03-02T12:52:15Z | - |
dc.date.issued | 1986 | - |
dc.identifier.uri | http://hdl.handle.net/2445/151628 | - |
dc.description | Preprint enviat per a la seva publicació en una revista científica: Manuscripta Math 57, 469–475 (1987). [https://doi.org/10.1007/BF01168672] | ca |
dc.description.abstract | 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. | ca |
dc.format.extent | 7 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | ca |
dc.publisher | Universitat de Barcelona | ca |
dc.relation.isformatof | Reproducció digital del document original en paper [CRAI Biblioteca de Matemàtiques i Informàtica - Dipòsit Departament CAIXA 31.33] | - |
dc.relation.ispartofseries | Mathematics Preprint Series; 45 | ca |
dc.rights | (c) Angela Arenas, 1986 | - |
dc.source | Preprints de Matemàtiques - Mathematics Preprint Series | - |
dc.subject.classification | Geometria algebraica | - |
dc.subject.other | Universitat de Barcelona. Institut de Matemàtica | - |
dc.title | On the summation of the singular series | ca |
dc.type | info:eu-repo/semantics/article | ca |
dc.type | info:eu-repo/semantics/submittedVersion | - |
dc.identifier.dl | DL B 22342-1986 | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Preprints de Matemàtiques - Mathematics Preprint Series |
Files in This Item:
File | Description | Size | Format | |
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MPS_N045.pdf | 225.49 kB | Adobe PDF | View/Open |
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