Quadratic integral solutions to double Pell equations
Francesco Veneziano (2011)
Rendiconti del Seminario Matematico della Università di Padova
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Francesco Veneziano (2011)
Rendiconti del Seminario Matematico della Università di Padova
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Richard Lakein (1972)
Acta Arithmetica
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Pilar Bayer, Jordi Guàrdia (2005)
Journal de Théorie des Nombres de Bordeaux
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Shimura curves associated to rational nonsplit quaternion algebras are coarse moduli spaces for principally polarized abelian surfaces endowed with quaternionic multiplication. These objects are also known as . We present a method for computing equations for genus 2 curves whose Jacobian is a fake elliptic curve with complex multiplication. The method is based on the explicit knowledge of the normalized period matrices and on the use of theta functions with characteristics. As in the...
Mollin, R. (2001)
Serdica Mathematical Journal
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We investigate infinite families of integral quadratic polynomials {fk (X)} k∈N and show that, for a fixed k ∈ N and arbitrary X ∈ N, the period length of the simple continued fraction expansion of √fk (X) is constant. Furthermore, we show that the period lengths of √fk (X) go to infinity with k. For each member of the families involved, we show how to determine, in an easy fashion, the fundamental unit of the underlying quadratic field. We also demonstrate how the simple continued...
Stéphane Louboutin (1997)
Acta Arithmetica
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Hui Lin Zhu, Jian Hua Chen (2008)
Rendiconti del Seminario Matematico della Università di Padova
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Young-Ho Park, Soun-Hi Kwon (1998)
Acta Arithmetica
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Daniel Shanks, Peter Weinberger (1972)
Acta Arithmetica
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