Sur les entiers n pour lesquels il y à beaucoup de groupes abéliens d'ordre \(n\)

DOI10.5802/aif.714zbMath0363.10027OpenAlexW2324367983MaRDI QIDQ1240271

Jean Louis Nicolas

Publication date: 1978

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1978__28_4_1_0

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Elementary theory of partitions (11P81) Distribution of primes (11N05)

Related Items (30)

Log-concavity of infinite product generating functions ⋮ Limits of Jensen polynomials for partitions and other sequences ⋮ Hyperbolicity of Appell polynomials of functions in the \(\delta \)-Laguerre-Pólya class ⋮ Probabilistic divide-and-conquer: deterministic second half ⋮ Exact formulae for the fractional partition functions ⋮ Laguerre inequalities for discrete sequences ⋮ Turán inequalities for \(k\)-th power partition functions ⋮ Turán inequalities for the broken \(k\)-diamond partition functions ⋮ Inequalities for the overpartition function arising from determinants ⋮ A unified framework to prove multiplicative inequalities for the partition function ⋮ Higher order Turán inequalities for the distinct partition function ⋮ Log-concavity of the restricted partition function \(p_{\mathcal{A}}(n, k)\) and the new Bessenrodt-Ono type inequality ⋮ Log concavity for unimodal sequences ⋮ Eventual log-concavity of \(k\)-rank statistics for integer partitions ⋮ Higher order Turán inequalities for \(k\)-regular partitions ⋮ Log-concavity of infinite product and infinite sum generating functions ⋮ Inequalities for plane partitions ⋮ Probabilistic Divide-and-Conquer: A New Exact Simulation Method, With Integer Partitions as an Example ⋮ Higher order Laguerre inequalities for the partition function ⋮ Inequalities for the broken \(k\)-diamond partition functions ⋮ A note on the higher order Turán inequalities for \(k\)-regular partitions ⋮ On the number of Abelian groups of a given order and on certain related multiplicative functions ⋮ The asymptotic distribution of the rank for unimodal sequences ⋮ Polynomization of the Chern-Fu-Tang conjecture ⋮ Proof of the Bessenrodt-Ono inequality by induction ⋮ Hyperbolicity of the partition Jensen polynomials ⋮ Turán inequalities for the plane partition function ⋮ On a new class of Laguerre-Pólya type functions with applications in number theory ⋮ Fractional partitions and conjectures of Chern–Fu–Tang and Heim–Neuhauser ⋮ Positivity of the determinants of the partition function and the overpartition function

Cites Work

• The maximal number of non-isomorphic abelian groups of order \(n\)
• Die maximale Ordnung primzahl-unabhängiger multiplikativer Funktionen
• Über die Anzahl Abelscher Gruppen gegebener Ordnung.
• Formes modulaires de poids $1$
• DIE MAXIMALE ORDNUNG DER ANZAHL DER WESENTLICH VERSCHIEDENEN ABELSCHEN GRUPPEN n-TER ORDNUNG
• Répartition Des Nombres Hautement Composés de Ramanujan
• On the number of Abelian groups of a given order
• Arithmetical properties of finite rings and algebras, and analytic number theory.
• A Prime-Divisor Function
• ON THE NUMBER OF ABELIAN GROUPS OF A GIVEN ORDER
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