Hyperelliptic Curves, Continued Fractions and Somos Sequences

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A pseudo-elliptic integral Z x 6t p t 4 + 4t 3 − 6t 2 + 4t + 1 dt Two Surprising Allegations “ = log x 6 + 12x 5 + 45x 4 + 44x 3 − 33x 2 + 43 +(x 4 + 10x 3 + 30x 2 p + 22x − 11) A <strong>Somos</strong> sequence of width 5 x 4 + 4x 3 − 6x 2 + 4x + 1 The sequence (Bh)−∞
A pseudo-elliptic integral Z x 6t p t 4 + 4t 3 − 6t 2 + 4t + 1 dt Two Surprising Allegations “ = log x 6 + 12x 5 + 45x 4 + 44x 3 − 33x 2 + 43 +(x 4 + 10x 3 + 30x 2 p + 22x − 11) A <strong>Somos</strong> sequence of width 5 x 4 + 4x 3 − 6x 2 + 4x + 1 The sequence (Bh)−∞
Page 1: Hyperelliptic Curves, Continued Fra
Page 5 and 6: A pseudo-elliptic integral Z x 6t p
Page 7 and 8: A pseudo-elliptic integral Z x 6t p
Page 9 and 10: Michael Somos’s Sequences The sto
Page 17 and 18: Concerning (Bh) — thus 5-Somos
Page 25 and 26: The surprising integral Z X 6t dt p
Page 31 and 32: Plainly, the equations detailing ps
Page 43 and 44: Moreover, u ′ = a ′ + b ′√
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Units and Torsion The notion unit e
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Units in Quadratic Fields and Conti
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Continued Fraction of the Square Ro
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To detail the continued fraction ex
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There is a minor miracle. Because t
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I should point out that any actual
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Second, if we replace D by D + 1 th
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Second, if we replace D by D + 1 th
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In the course of studying continued
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In the course of studying continued
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What the Continued Fraction Does No
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The elliptic case When g = 1 we hav
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The −dh are in fact the abscissæ
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As it happens, a combinatorial/alge
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Elliptic Divisibility Sequences Now
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Remarkably, Ward introduces his seq
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Elliptic Division Polynomials I ins
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4-Somos Suppose (Ch) = (. . . , 2,
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Higher Genus There surely are analo
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Others can do worse, and better. If
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Others can do worse, and better. If
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A cute example à la Somos Whatever
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A cute example à la Somos Whatever
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References Rather than attempt a li
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Hyperelliptic Curves, Continued Fractions and Somos Sequences

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