CERTAIN VALUES OF GAUSSIAN HYPERGEOMETRIC SERIES AND A FAMILY OF ALGEBRAIC CURVES
نویسندگان
چکیده
منابع مشابه
Values of Gaussian Hypergeometric Series
Let p be prime and let GF (p) be the finite field with p elements. In this note we investigate the arithmetic properties of the Gaussian hypergeometric functions 2F1(x) =2 F1 „ φ, φ | x « and 3F2(x) =3 F2 „ φ, φ, φ , | x « where φ and respectively are the quadratic and trivial characters of GF (p). For all but finitely many rational numbers x = λ, there exist two elliptic curves 2E1(λ) and 3E2(...
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The hypergeometric functions nFn−1 are higher transcendental functions, but for certain parameter values they become algebraic. This occurs, e.g., if the defining hypergeometric differential equation has irreducible but imprimitive monodromy. It is shown that many algebraic nFn−1’s of this type can be represented as combinations of certain explicitly algebraic functions of a single variable, i....
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2012
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s179304211250056x