On the length of the continued fraction for values of quotients of power sums

Pietro Corvaja[1]; Umberto Zannier[2]

  • [1] Dipartimento di Matematica Università di Udine via delle Scienze 206 33100 Udine (Italy)
  • [2] Scuola Normale Superiore Piazza dei Cavalieri, 7 56100 Pisa (Italy)

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 3, page 737-748
  • ISSN: 1246-7405

Abstract

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Generalizing a result of Pourchet, we show that, if α , β are power sums over ℚ satisfying suitable necessary assumptions, the length of the continued fraction for α ( n ) / β ( n ) tends to infinity as n → ∞ . This will be derived from a uniform Thue-type inequality for the rational approximations to the rational numbers α ( n ) / β ( n ) , n ∈ ℕ .

How to cite

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Corvaja, Pietro, and Zannier, Umberto. "On the length of the continued fraction for values of quotients of power sums." Journal de Théorie des Nombres de Bordeaux 17.3 (2005): 737-748. <http://eudml.org/doc/249440>.

@article{Corvaja2005,
abstract = {Generalizing a result of Pourchet, we show that, if $\alpha ,\beta $ are power sums over $\mathbb\{Q\}$ satisfying suitable necessary assumptions, the length of the continued fraction for $\alpha (n)/\beta (n)$ tends to infinity as $n\rightarrow \infty $. This will be derived from a uniform Thue-type inequality for the rational approximations to the rational numbers $\alpha (n)/\beta (n)$, $n\in \mathbb\{N\}$.},
affiliation = {Dipartimento di Matematica Università di Udine via delle Scienze 206 33100 Udine (Italy); Scuola Normale Superiore Piazza dei Cavalieri, 7 56100 Pisa (Italy)},
author = {Corvaja, Pietro, Zannier, Umberto},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Continued fractions; Power sums; Applications of the subspace theorem},
language = {eng},
number = {3},
pages = {737-748},
publisher = {Université Bordeaux 1},
title = {On the length of the continued fraction for values of quotients of power sums},
url = {http://eudml.org/doc/249440},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Corvaja, Pietro
AU - Zannier, Umberto
TI - On the length of the continued fraction for values of quotients of power sums
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 3
SP - 737
EP - 748
AB - Generalizing a result of Pourchet, we show that, if $\alpha ,\beta $ are power sums over $\mathbb{Q}$ satisfying suitable necessary assumptions, the length of the continued fraction for $\alpha (n)/\beta (n)$ tends to infinity as $n\rightarrow \infty $. This will be derived from a uniform Thue-type inequality for the rational approximations to the rational numbers $\alpha (n)/\beta (n)$, $n\in \mathbb{N}$.
LA - eng
KW - Continued fractions; Power sums; Applications of the subspace theorem
UR - http://eudml.org/doc/249440
ER -

References

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