Establishing the minimal index in a parametric family of bicyclic biquadratic fields. (English) Zbl 1265.11061

Jadrijević, Borka

Period. Math. Hung. 58, No. 2, 155-180 (2009).

Summary: Let \(c \geq 3\) be a positive integer such that \(c, 4c+1, c-1\) are square-free integers relatively prime in pairs. In this paper we find the minimal index and determine all elements with minimal index in the bicyclic biquadratic field \(K = {\mathbb Q} \left( \sqrt{\left( 4c+1 \right) c}, \sqrt{\left( c-1 \right) c} \right)\).

MSC:

11D57	Multiplicative and norm form equations
11A55	Continued fractions
11B37	Recurrences
11J68	Approximation to algebraic numbers
11J86	Linear forms in logarithms; Baker’s method
11Y50	Computer solution of Diophantine equations

Keywords:

index form equations; minimal index; totally real bicyclic biquadratic fields; simultaneous Pellian equations

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