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ALGEBRAIC NUMBERS, TRANSCENDENTAL NUMBERS AND ELLIPTIC CURVES DERIVED FROM INFINITE PRODUCTS
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 Title & Authors
ALGEBRAIC NUMBERS, TRANSCENDENTAL NUMBERS AND ELLIPTIC CURVES DERIVED FROM INFINITE PRODUCTS
Kim, Dae-Yeoul; Koo, Ja-Kyung;
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 Abstract
Let k be an imaginary quadratic field, η the complex upper half plane, and let η , p = . In this article, using the infinite product formulas for g2 and g3, we prove that values of certain infinite products are transcendental whenever are imaginary quadratic. And we derive analogous results of Berndt-Chan-Zhang ([4]). Also we find the values of (equation omitted) when we know j(). And we construct an elliptic curve E : = + 3 + {3-(j/256)}x + 1 with j = j() 0 and P = (equation omitted) E.
 Keywords
infinite product;transcendental number;elliptic curve;
 Language
English
 Cited by
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