Exponential sums and the abelian group problem
type: Item
instance of: scholarly article
title: Exponential sums and the abelian group problem
zbMATH Open document ID: 1219.11144
author: Hongquan Liu
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 2010-07-20T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.facm/1277811635
review text: Let \(A(x)\) be the number of isomorphism classes of abelian groups of orders \(\leq x\). Using the method of exponential sums, the author proves that for \(x>10\) \[ A(x)=C_1x+C_2x^{\frac 12}+C_3x^{\frac 13}+O(x^{\frac14}e^{V(x)}), \] with explicit constants \(C_1,C_2,C_3\) and \[ V(x)=\frac{1}{\sqrt{3}}(\log x\log\log x)^{\frac12}+O((\log x)^{\frac12}(\log\log x)^{-\frac12}). \]
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11N45
Mathematics Subject Classification ID: 11L07
zbMATH DE Number: 5758459
zbMATH Keywords: abelian groups
zbMATH Keywords: exponential sums
MaRDI profile type: Publication
OpenAlex ID: W2005304292
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DOI: 10.7169/FACM/1277811635
description: scientific article; zbMATH DE number 5758459