On unit fractions with denominators in short intervals
Ernest S. Croot III (2001)
Acta Arithmetica
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Ernest S. Croot III (2001)
Acta Arithmetica
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Amedeo Scremin (2006)
Acta Arithmetica
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Bruce C. Berndt, Sun Kim, M. Tip Phaovibul, Alexandru Zaharescu (2013)
Acta Arithmetica
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We study the question: How often do partial sums of power series of functions coalesce with convergents of the (simple) continued fractions of the functions? Our theorems quantitatively demonstrate that the answer is: not very often. We conjecture that in most cases there are only a finite number of partial sums coinciding with convergents. In many of these cases, we offer exact numbers in our conjectures.
Igor E. Shparlinski (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
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For positive integers m and N, we estimate the rational exponential sums with denominator m over the reductions modulo m of elements of the set ℱ(N) = {s/r : r,s ∈ ℤ, gcd(r,s) = 1, N ≥ r > s ≥ 1} of Farey fractions of order N (only fractions s/r with gcd(r,m) = 1 are considered).
Dean Hickerson (1977)
Journal für die reine und angewandte Mathematik
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Munagi, Augustine O. (2007)
Integers
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Komatsu, Takao (2004)
Mathematica Pannonica
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Denis, Remy Y. (1990)
International Journal of Mathematics and Mathematical Sciences
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Walter Philipp (1988)
Monatshefte für Mathematik
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Henry Cohn (1996)
Acta Arithmetica
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Chan, Hei-Chi (2004)
International Journal of Mathematics and Mathematical Sciences
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Florin P. Boca, Joseph Vandehey (2012)
Acta Arithmetica
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Komatsu, Takao (2006)
Mathematica Pannonica
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Boonrod Yuttanan (2012)
Acta Arithmetica
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