On sharp transitions in making squares

DOI10.4007/annals.2012.175.3.10zbMath1321.11122arXiv0811.0372OpenAlexW2149314352WikidataQ106094314 ScholiaQ106094314MaRDI QIDQ431647

Ernie Croot, Robin Pemantle, Prasad Tetali, Andrew Granville

Publication date: 29 June 2012

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.0372

zbMATH Keywords

sievingfactorization algorithmsmooth numbersrandom hypergraphDixon's random squares algorithmsmooth number estimatessquare product

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Factorization (11Y05)

Related Items (8)

The Most Frequent Values of the Largest Prime Divisor Function ⋮ The sharp threshold for making squares ⋮ Small cores in 3-uniform hypergraphs ⋮ Running Time Predictions for Factoring Algorithms ⋮ Orienteering with one endomorphism ⋮ A problem of Erdős–Graham–Granville–Selfridge on integral points on hyperelliptic curves ⋮ Counting primitive subsets and other statistics of the divisor graph of \(\{1,2,\dots,n\}\) ⋮ Rigorous analysis of a randomised number field sieve

Cites Work

• Enumerative problems inspired by Mayer's theory of cluster integrals
• Large character sums
• Running Time Predictions for Factoring Algorithms
• On Integers Free of Large Prime Factors
• The Multiple Polynomial Quadratic Sieve
• Asymptotically Fast Factorization of Integers
• Sharp thresholds of graph properties, and the $k$-sat problem
• Dependent Sets of Constant Weight Binary Vectors
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