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Displaying similar documents to “Norm form equations and continued fractions.”

On subsequences of convergents to a quadratic irrational given by some numerical schemes

Benoît Rittaud (2010)

Journal de Théorie des Nombres de Bordeaux

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Given a quadratic irrational α , we are interested in how some numerical schemes applied to a convenient function f provide subsequences of convergents to α . We investigate three numerical schemes: secant-like methods and formal generalizations, which lead to linear recurring subsequences; the false position method, which leads to arithmetical subsequences of convergents and gives some interesting series expansions; Newton’s method, for which we complete a result of Edward Burger [] about...

On wild ramification in quaternion extensions

G. Griffith Elder, Jeffrey J. Hooper (2007)

Journal de Théorie des Nombres de Bordeaux

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This paper provides a complete catalog of the break numbers that occur in the ramification filtration of fully and thus wildly ramified quaternion extensions of dyadic number fields which contain - 1 (along with some partial results for the more general case). This catalog depends upon the , which as defined in [] is associated with the biquadratic subfield. Moreover we find that quaternion counter-examples to the conclusion of the Hasse-Arf Theorem are extremely rare and can occur only...

Rational approximations to 2 3 and other algebraic numbers revisited

Paul M. Voutier (2007)

Journal de Théorie des Nombres de Bordeaux

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In this paper, we establish improved effective irrationality measures for certain numbers of the form n 3 , using approximations obtained from hypergeometric functions. These results are very close to the best possible using this method. We are able to obtain these results by determining very precise arithmetic information about the denominators of the coefficients of these hypergeometric functions. Improved bounds for the Chebyshev functions in arithmetic progressions θ ( k , l ; x ) and...