On the period of the continued fraction for values of the square root of power sums
Amedeo Scremin (2006)
Acta Arithmetica
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Amedeo Scremin (2006)
Acta Arithmetica
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Ernest S. Croot III (2001)
Acta Arithmetica
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R. R. Hall, M. N. Huxley (1993)
Acta Arithmetica
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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).
Walter Philipp (1988)
Monatshefte für Mathematik
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Boonrod Yuttanan (2012)
Acta Arithmetica
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Dean Hickerson (1977)
Journal für die reine und angewandte Mathematik
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Henry Cohn (1996)
Acta Arithmetica
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Florin P. Boca, Joseph Vandehey (2012)
Acta Arithmetica
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P. Shiu (1996)
Publications de l'Institut Mathématique
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Yong-Gao Chen, Christian Elsholtz, Li-Li Jiang (2012)
Acta Arithmetica
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Zongduo Dai, Ping Wang, Kunpeng Wang, Xiutao Feng (2007)
Acta Arithmetica
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S. G. Dani (2015)
Acta Arithmetica
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We introduce a general framework for studying continued fraction expansions for complex numbers, and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial quotients in a discrete subring of ℂ an analogue of the classical Lagrange theorem, characterising quadratic surds as numbers with eventually periodic continued fraction expansions, is proved. Monotonicity and exponential growth are established for the...
Xue Hai Hu, Jun Wu (2009)
Acta Arithmetica
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Takao Komatsu (2003)
Acta Arithmetica
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Denis, Remy Y. (1990)
International Journal of Mathematics and Mathematical Sciences
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