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Lattice Points Close to a Smooth Curve and Squarefull Numbers in Short Intervals
Author(s) -
Trifonov Ognian
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610701002939
Subject(s) - mathematics , lattice (music) , upper and lower bounds , combinatorics , mathematical analysis , physics , acoustics
An approach of Swinnerton‐Dyer is extended to obtain new upper bounds for the number of lattice points close to a smooth curve. One consequence of these bounds is a new asymptotic result for the distribution of squarefull numbers in short intervals.