Square-full numbers in short intervals
1991 ◽
Vol 110
(1)
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pp. 1-3
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Keyword(s):
A positive integer n is called square-full if p2|n for every prime factor p of n. Let Q(x) denote the number of square-full integers up to x. It was shown by Bateman and Grosswald [1] thatBateman and Grosswald also remarked that any improvement in the exponent would imply a ‘quasi-Riemann Hypothesis’ of the type for . Thus (1) is essentially as sharp as one can hope for at present. From (1) it follows that, for the number of square-full integers in a short interval, we havewhen and y = o (x½). (It seems more suggestive) to write the interval as (x, x + x½y]) than (x, x + y], since only intervals of length x½ or more can be of relevance here.)
Keyword(s):
1991 ◽
Vol 109
(1)
◽
pp. 1-5
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Keyword(s):
1984 ◽
Vol 25
(1)
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pp. 127-134
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2009 ◽
Vol 79
(3)
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pp. 455-463
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Keyword(s):
2018 ◽
Vol 107
(1)
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pp. 133-144
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Keyword(s):
1996 ◽
Vol 119
(2)
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pp. 201-208
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2010 ◽
Vol 53
(2)
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pp. 293-299
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1961 ◽
Vol 5
(1)
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pp. 35-40
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1955 ◽
Vol 7
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pp. 347-357
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