Density of solutions to quadratic congruences

dc.contributor.author	PRABHU, NEHA	en_US
dc.date.accessioned	2019-07-01T05:37:44Z
dc.date.available	2019-07-01T05:37:44Z
dc.date.issued	2017-06	en_US
dc.identifier.citation	Czechoslovak Mathematical Journal, 67(2), 439-455.	en_US
dc.identifier.issn	0011-4642	en_US
dc.identifier.issn	1572-9141	en_US
dc.identifier.uri	http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/3360
dc.identifier.uri	https://doi.org/10.21136/CMJ.2017.0712-15	en_US
dc.description.abstract	A classical result in number theory is Dirichlet's theorem on the density of primes in an arithmetic progression. We prove a similar result for numbers with exactly k prime factors for k > 1. Building upon a proof by E.M. Wright in 1954, we compute the natural density of such numbers where each prime satisfies a congruence condition. As an application, we obtain the density of squarefree n <= x with k prime factors such that a fixed quadratic equation has exactly 2 k solutions modulo n.	en_US
dc.language.iso	en	en_US
dc.publisher	Springer Nature	en_US
dc.subject	Dirichlet's theorem	en_US
dc.subject	Asymptotic density	en_US
dc.subject	Primes in arithmetic	en_US
dc.subject	Progression squarefree number	en_US
dc.subject	2017	en_US
dc.title	Density of solutions to quadratic congruences	en_US
dc.type	Article	en_US
dc.contributor.department	Dept. of Mathematics	en_US
dc.identifier.sourcetitle	Czechoslovak Mathematical Journal	en_US
dc.publication.originofpublisher	Foreign	en_US