Exponential sums, number of solutions of algebraic equations, and poincaré series

Definitions of Gauss and Ramanujan sums over the algebras A and Lv are given, and their main properties are proved. Using these results an analogous of an old result of Libri on the number of solutions of algebraic equations with integral coecients modulo a prime power is obtained, and then used to...

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Autores:
Albis González, Víctor Samuel
Carvajal, Edilmo
Tipo de recurso:
Article of journal
Fecha de publicación:
2010
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/73786
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/73786
http://bdigital.unal.edu.co/38263/
Palabra clave:
Gauss sums
Ramanujan sums
number of solutions of algebraic equations over
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Albis González, Víctor Samuelea5d56fa-a0e5-4222-b928-0501cb48afbc300Carvajal, Edilmobb2cc4ac-0645-424d-ba14-f3865f578a233002019-07-03T16:50:26Z2019-07-03T16:50:26Z2010https://repositorio.unal.edu.co/handle/unal/73786http://bdigital.unal.edu.co/38263/Definitions of Gauss and Ramanujan sums over the algebras A and Lv are given, and their main properties are proved. Using these results an analogous of an old result of Libri on the number of solutions of algebraic equations with integral coecients modulo a prime power is obtained, and then used to compute the number of solutions of some equations with coecients in Lv. Finally, an analogous of a problem of Nageswara Rao on algebraic equations subject to partitions is solved for equationswith coecients in Lv.application/pdfspaBoletín de Matemáticashttp://revistas.unal.edu.co/index.php/bolma/article/view/40803Universidad Nacional de Colombia Revistas electrónicas UN Boletín de MatemáticasBoletín de MatemáticasBoletín de Matemáticas; Vol. 17, núm. 2 (2010); 165-192 Boletín de Matemáticas; Vol. 17, núm. 2 (2010); 165-192 2357-6529 0120-0380Albis González, Víctor Samuel and Carvajal, Edilmo (2010) Exponential sums, number of solutions of algebraic equations, and poincaré series. Boletín de Matemáticas; Vol. 17, núm. 2 (2010); 165-192 Boletín de Matemáticas; Vol. 17, núm. 2 (2010); 165-192 2357-6529 0120-0380 .Exponential sums, number of solutions of algebraic equations, and poincaré seriesArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTGauss sumsRamanujan sumsnumber of solutions of algebraic equations overORIGINAL40803-183733-1-PB.pdfapplication/pdf158084https://repositorio.unal.edu.co/bitstream/unal/73786/1/40803-183733-1-PB.pdf35b9bddfec69ce068f337cec9e7f66acMD51THUMBNAIL40803-183733-1-PB.pdf.jpg40803-183733-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg4885https://repositorio.unal.edu.co/bitstream/unal/73786/2/40803-183733-1-PB.pdf.jpg3bb2fb98fe8b660705188a107fcfbb90MD52unal/73786oai:repositorio.unal.edu.co:unal/737862024-06-26 23:10:34.204Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Exponential sums, number of solutions of algebraic equations, and poincaré series
title Exponential sums, number of solutions of algebraic equations, and poincaré series
spellingShingle Exponential sums, number of solutions of algebraic equations, and poincaré series
Gauss sums
Ramanujan sums
number of solutions of algebraic equations over
title_short Exponential sums, number of solutions of algebraic equations, and poincaré series
title_full Exponential sums, number of solutions of algebraic equations, and poincaré series
title_fullStr Exponential sums, number of solutions of algebraic equations, and poincaré series
title_full_unstemmed Exponential sums, number of solutions of algebraic equations, and poincaré series
title_sort Exponential sums, number of solutions of algebraic equations, and poincaré series
dc.creator.fl_str_mv Albis González, Víctor Samuel
Carvajal, Edilmo
dc.contributor.author.spa.fl_str_mv Albis González, Víctor Samuel
Carvajal, Edilmo
dc.subject.proposal.spa.fl_str_mv Gauss sums
Ramanujan sums
number of solutions of algebraic equations over
topic Gauss sums
Ramanujan sums
number of solutions of algebraic equations over
description Definitions of Gauss and Ramanujan sums over the algebras A and Lv are given, and their main properties are proved. Using these results an analogous of an old result of Libri on the number of solutions of algebraic equations with integral coecients modulo a prime power is obtained, and then used to compute the number of solutions of some equations with coecients in Lv. Finally, an analogous of a problem of Nageswara Rao on algebraic equations subject to partitions is solved for equationswith coecients in Lv.
publishDate 2010
dc.date.issued.spa.fl_str_mv 2010
dc.date.accessioned.spa.fl_str_mv 2019-07-03T16:50:26Z
dc.date.available.spa.fl_str_mv 2019-07-03T16:50:26Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/73786
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/38263/
url https://repositorio.unal.edu.co/handle/unal/73786
http://bdigital.unal.edu.co/38263/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv http://revistas.unal.edu.co/index.php/bolma/article/view/40803
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Boletín de Matemáticas
Boletín de Matemáticas
dc.relation.ispartofseries.none.fl_str_mv Boletín de Matemáticas; Vol. 17, núm. 2 (2010); 165-192 Boletín de Matemáticas; Vol. 17, núm. 2 (2010); 165-192 2357-6529 0120-0380
dc.relation.references.spa.fl_str_mv Albis González, Víctor Samuel and Carvajal, Edilmo (2010) Exponential sums, number of solutions of algebraic equations, and poincaré series. Boletín de Matemáticas; Vol. 17, núm. 2 (2010); 165-192 Boletín de Matemáticas; Vol. 17, núm. 2 (2010); 165-192 2357-6529 0120-0380 .
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Boletín de Matemáticas
institution Universidad Nacional de Colombia
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