On Diophantine Systems with Sum of Squares and Linear Form Satisfying a Congruential Condition of a Special Form

An asymptotic formula with a residual term is obtained for the number of solutions of a Diophantine system containing the sum of squares of variables, as well as a linear form, and each solution of the system satisfies a congruential condition of a special kind. In addition, in the case of an even n...

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Главные авторы:	Pachev, U. M., Пачев, У. М., Dokhov, R. A., Дохов, Р. А.
Формат:	Статья
Язык:	English
Опубликовано:	Springer Science and Business Media Deutschland GmbH 2024
Темы:	Diophantine system with sum of squares Special series of Diophantine system Linear form Asymptotic formula Congruences of the second degree Congruential condition
Online-ссылка:	https://dspace.ncfu.ru/handle/123456789/29201
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spelling	ir-123456789-292012024-11-05T09:56:54Z On Diophantine Systems with Sum of Squares and Linear Form Satisfying a Congruential Condition of a Special Form Pachev, U. M. Пачев, У. М. Dokhov, R. A. Дохов, Р. А. Diophantine system with sum of squares Special series of Diophantine system Linear form Asymptotic formula Congruences of the second degree Congruential condition An asymptotic formula with a residual term is obtained for the number of solutions of a Diophantine system containing the sum of squares of variables, as well as a linear form, and each solution of the system satisfies a congruential condition of a special kind. In addition, in the case of an even number of variables an upper estimate is given for the special series of the Diophantine system under study, relying on the formula for the number of solutions of congruences of the second degree modulo the power of a prime number. 2024-11-05T09:55:30Z 2024-11-05T09:55:30Z 2024 Статья Pachev U., Dokhov R., Kodzokov A. On Diophantine Systems with Sum of Squares and Linear Form Satisfying a Congruential Condition of a Special Form // Lecture Notes in Networks and Systems. - 2024. - 1044 LNNS. - pp. 3 - 10. - DOI: 10.1007/978-3-031-64010-0_1 https://dspace.ncfu.ru/handle/123456789/29201 en Lecture Notes in Networks and Systems application/pdf Springer Science and Business Media Deutschland GmbH
institution	СКФУ
collection	Репозиторий
language	English
topic	Diophantine system with sum of squares Special series of Diophantine system Linear form Asymptotic formula Congruences of the second degree Congruential condition
spellingShingle	Diophantine system with sum of squares Special series of Diophantine system Linear form Asymptotic formula Congruences of the second degree Congruential condition Pachev, U. M. Пачев, У. М. Dokhov, R. A. Дохов, Р. А. On Diophantine Systems with Sum of Squares and Linear Form Satisfying a Congruential Condition of a Special Form
description	An asymptotic formula with a residual term is obtained for the number of solutions of a Diophantine system containing the sum of squares of variables, as well as a linear form, and each solution of the system satisfies a congruential condition of a special kind. In addition, in the case of an even number of variables an upper estimate is given for the special series of the Diophantine system under study, relying on the formula for the number of solutions of congruences of the second degree modulo the power of a prime number.
format	Статья
author	Pachev, U. M. Пачев, У. М. Dokhov, R. A. Дохов, Р. А.
author_facet	Pachev, U. M. Пачев, У. М. Dokhov, R. A. Дохов, Р. А.
author_sort	Pachev, U. M.
title	On Diophantine Systems with Sum of Squares and Linear Form Satisfying a Congruential Condition of a Special Form
title_short	On Diophantine Systems with Sum of Squares and Linear Form Satisfying a Congruential Condition of a Special Form
title_full	On Diophantine Systems with Sum of Squares and Linear Form Satisfying a Congruential Condition of a Special Form
title_fullStr	On Diophantine Systems with Sum of Squares and Linear Form Satisfying a Congruential Condition of a Special Form
title_full_unstemmed	On Diophantine Systems with Sum of Squares and Linear Form Satisfying a Congruential Condition of a Special Form
title_sort	on diophantine systems with sum of squares and linear form satisfying a congruential condition of a special form
publisher	Springer Science and Business Media Deutschland GmbH
publishDate	2024
url	https://dspace.ncfu.ru/handle/123456789/29201
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On Diophantine Systems with Sum of Squares and Linear Form Satisfying a Congruential Condition of a Special Form

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