کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4665899 | 1633835 | 2014 | 53 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The uniformization of certain algebraic hypergeometric functions
ترجمه فارسی عنوان
یکنواختی برخی از توابع هیپر ژئومتریک جبری
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
The hypergeometric functions Fnâ1n are higher transcendental functions, but for certain parameter values they become algebraic, because the monodromy of the defining hypergeometric differential equation becomes finite. It is shown that many algebraic Fnâ1nʼs, for which the finite monodromy is irreducible but imprimitive, can be represented as combinations of certain explicitly algebraic functions of a single variable; namely, the roots of trinomials. This generalizes a result of Birkeland, and is derived as a corollary of a family of binomial coefficient identities that is of independent interest. Any tuple of roots of a trinomial traces out a projective algebraic curve, and it is also determined when this so-called Schwarz curve is of genus zero and can be rationally parametrized. Any such parametrization yields a hypergeometric identity that explicitly uniformizes a family of algebraic Fnâ1nʼs. Many examples of such uniformizations are worked out explicitly. Even when the governing Schwarz curve is of positive genus, it is shown how it is sometimes possible to construct explicit single-valued or multivalued parametrizations of individual algebraic Fnâ1nʼs, by parametrizing a quotiented Schwarz curve. The parametrization requires computations in rings of symmetric polynomials.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 253, 1 March 2014, Pages 86-138
Journal: Advances in Mathematics - Volume 253, 1 March 2014, Pages 86-138
نویسندگان
Robert S. Maier,