Fast computation of the number of solutions to x12+ ··· + xk2 = ¿ (mod n)
Grau, J.M. ; Oller-Marcén, A.M.
Resumen: In this paper we study the multiplicative function ¿k,¿(n) that counts the number of solutions of the equation x1 2+...+xk 2=¿(modn) in (Z/nZ)k. In particular we give closed explicit formulas for ¿k,¿(ps). This leads to an algorithm with an arithmetic complexity of constant order that improves previous work by Tóth [10] and completes the quadratic case considered by Li and Ouyang in [8].
Idioma: Inglés
DOI: 10.1016/j.jnt.2018.09.015
Año: 2018
Publicado en: JOURNAL OF NUMBER THEORY 200 (2018), 427 - 440
ISSN: 0022-314X
Factor impacto JCR: 0.684 (2018)
Categ. JCR: MATHEMATICS rank: 181 / 313 = 0.578 (2018) - Q3 - T2
Factor impacto SCIMAGO: 0.837 - Algebra and Number Theory (Q1)
Tipo y forma: Article (PostPrint)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material.
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Idioma: Inglés
DOI: 10.1016/j.jnt.2018.09.015
Año: 2018
Publicado en: JOURNAL OF NUMBER THEORY 200 (2018), 427 - 440
ISSN: 0022-314X
Factor impacto JCR: 0.684 (2018)
Categ. JCR: MATHEMATICS rank: 181 / 313 = 0.578 (2018) - Q3 - T2
Factor impacto SCIMAGO: 0.837 - Algebra and Number Theory (Q1)
Tipo y forma: Article (PostPrint)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material. Exportado de SIDERAL (2020-05-13-00:50:33)
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Record created 2019-10-25, last modified 2020-05-13