2017/02/08 by Ansar El Hassani, Hassani, Ansar El
Computer Science · Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1702.03860
openalex publication_date 2017/02/08 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
In the first chapter, we will present a computation of the square value of\nthe module of L functions associated to a Dirichlet character. This computation\nsuggests to ask if a certain ring of arithmetic multiplicative functions exists\nand if it is unique. This search has led to the construction of that ring in\nchapter two. Finally, in the third chapter, we will present some propositions\nassociated with this ring. The result below is one of the main results of this\nwork :\n For F and G two completely multiplicative functions, s a complex number\nsuch as the dirichlet series D(F,s) and D(G,s) converge :\n \∀ F,G \∈ mathbbMc : D(F,s) \× D(G,s) = D(F \× G,2s)\n\× D(F square G,s) \n where the operation square is defined in chapter two as the sum of the\npreviously mentioned ring. Here are some similar versions, with s = x+iy :\n \∀ F, G \∈ mathbbMc : ~ D(F,s) \× D(G,\s) = D(F\n\× G,2x) \× D( fracF\Ideiy square\n fracG\Ide-iy, x) \n \∀ F, G \∈ mathbbMc : ~ |D(F,s)|2 = D(|F|2,2x) \×\nD( fracF\Ideiy square \ fracF\Ideiy,\nx) \n