Algebra of matrix arithmetic

DOI10.1006/jabr.1998.9999zbMath0921.15007OpenAlexW2092299235MaRDI QIDQ1276984

Olivier Ramaré, Gautami Bhowmik

Publication date: 15 September 1999

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1998.9999

zbMATH Keywords

integer matriceslatticesHall algebraHecke algebraSmith normal formpartitions of integersDirichlet convolution\(C\)-algebrasmatrix arithmeticalgebra of formal power seriesarithmetical functions of matricescyclic factorssubgroups of finite abelian groups

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Asymptotic results on arithmetic functions (11N37) Finite abelian groups (20K01) Arithmetic functions; related numbers; inversion formulas (11A25) Matrices of integers (15B36) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30) Matrices, determinants in number theory (11C20)

Cites Work

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• The ring of number-theoretic functions
• On the asymptotic behaviour of the number of subgroups of finite abelian groups
• The Hall polynomial
• Hecke algebras
• Left multiples and right divisors of integral matrices
• A Unimodality Result in the Enumeration of Subgroups of a Finite Abelian Group
• Some Generalizations of Ramanujan's Sum
• An Inequality for Invariant Factors
• Average orders of multiplicative arithmetical functions of integer matrices
• Subgroups of Abelian Groups
• Evaluation of divisor functions of matrices
• Über teilerfremde symmetrische Matrizenpaare.

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