The paper constructs generalized discrete Markov spectra for the family of equations x² + y² + z² + k1 yz + k2 zx + k3 xy = (3 + k1 + k2 + k3) xyz, with each spectrum element realized as both a Lagrange constant of a quadratic irrational and a Markov constant of an indefinite binary quadratic form.
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Generalized Markov-Hurwitz equations in n variables are introduced with extra interaction terms, and their positive integer solutions are shown to exhibit logarithmic asymptotics.
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Generalized discrete Markov spectra
The paper constructs generalized discrete Markov spectra for the family of equations x² + y² + z² + k1 yz + k2 zx + k3 xy = (3 + k1 + k2 + k3) xyz, with each spectrum element realized as both a Lagrange constant of a quadratic irrational and a Markov constant of an indefinite binary quadratic form.
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The Logarithmic Asymptotic Phenomenon for Generalized Markov-Hurwitz Equations
Generalized Markov-Hurwitz equations in n variables are introduced with extra interaction terms, and their positive integer solutions are shown to exhibit logarithmic asymptotics.