Periodicity Criterion for Continued Fractions of Key Elements in Hyperelliptic Fields

[1] Chebychev P. L.(1864)Sur l’integration de la differential J. Math. Pures Appl. 2 225-246

[2] Platonov V. P.(2014)Number-theoretic properties of hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves over the rational number field Russ. Math. Surv. 69 1-34

[3] Berry T. G.(1990)On periodicity of continued fractions in hyperelliptic function fields Arch. Math. 55 259-266

[4] Platonov V. P.(2018)On the problem of periodicity of continued fractions in hyperelliptic fields Sb. Math. 209 519-559

[5] Fedorov G. V.(2009)Groups of S-units in hyperelliptic fields and continued fractions Sb. Math. 200 1587-1615

[6] Benyash-Krivets V. V.(2018)Periodic continued fractions and S-units with second degree valuations in hyperelliptic fields Chebyshev. Sb. 19 282-297

[7] Platonov V. P.(2017)On the periodicity of continued fractions in hyperelliptic fields Dokl. Math. 95 254-258

[8] Fedorov G. V.(2017)On the periodicity of continued fractions in elliptic fields Dokl. Math. 96 332-335

[9] Platonov V. P.(2016)Continued rational fractions in hyperelliptic fields and the Mumford representation Dokl. Math. 94 692-696

[10] Fedorov G. V.(2018)Groups of S-units and the problem of periodicity of continued fractions in hyperelliptic fields Proc. Steklov Inst. Math. 302 336-357

[1] Chebychev P. L.(1864)Sur l’integration de la differential J. Math. Pures Appl. 2 225-246

[2] Platonov V. P.(2014)Number-theoretic properties of hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves over the rational number field Russ. Math. Surv. 69 1-34

[3] Berry T. G.(1990)On periodicity of continued fractions in hyperelliptic function fields Arch. Math. 55 259-266

[4] Platonov V. P.(2018)On the problem of periodicity of continued fractions in hyperelliptic fields Sb. Math. 209 519-559

[5] Fedorov G. V.(2009)Groups of S-units in hyperelliptic fields and continued fractions Sb. Math. 200 1587-1615

[6] Benyash-Krivets V. V.(2018)Periodic continued fractions and S-units with second degree valuations in hyperelliptic fields Chebyshev. Sb. 19 282-297

[7] Platonov V. P.(2017)On the periodicity of continued fractions in hyperelliptic fields Dokl. Math. 95 254-258

[8] Fedorov G. V.(2017)On the periodicity of continued fractions in elliptic fields Dokl. Math. 96 332-335

[9] Platonov V. P.(2016)Continued rational fractions in hyperelliptic fields and the Mumford representation Dokl. Math. 94 692-696

[10] Fedorov G. V.(2018)Groups of S-units and the problem of periodicity of continued fractions in hyperelliptic fields Proc. Steklov Inst. Math. 302 336-357