Výsledky vyhledávání - "Milne, Stephen C."

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Hankel determinants of Eisenstein series

Autor: Milne, Stephen C.

Publikováno v: in vol. 4 of Developments in Mathematics, Kluwer Academic Pub., Dordrecht, 2001, pp. 171--188.

In this paper we prove Garvan's conjectured formula for the square of the modular discriminant $\Delta$ as a 3 by 3 Hankel determinant of classical Eisenstein series $E_{2n}$. We then obtain similar formulas involving minors of Hankel determinants fo

Externí odkaz: http://arxiv.org/abs/math/0009130

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Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions

Autor: Milne, Stephen C.

Publikováno v: The Ramanujan Journal 6 (2002), 7--149. (Preface by George Andrews on pages 5--6.) Also in book as vol. 5 of ``Developments in Mathematics'', Kluwer Academic Pub., Dordrecht, 2002.

In this paper we derive many infinite families of explicit exact formulas involving either squares or triangular numbers, two of which generalize Jacobi's 4 and 8 squares identities to 4n^2 or 4n(n+1) squares, respectively, without using cusp forms.

Externí odkaz: http://arxiv.org/abs/math/0008068

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The $\bal$\ and $\bcl$\ Bailey Transform and Lemma

Autor: Milne, Stephen C., Lilly, Glenn M.

Publikováno v: Bull. Amer. Math. Soc. (N.S.) 26 (1992) 258-263

We announce a higher-dimensional generalization of the Bailey Transform, Bailey Lemma, and iterative ``Bailey chain'' concept in the setting of basic hypergeometric series very well-poised on unitary $A_{\ell}$ or symplectic $C_{\ell}$ groups. The cl

Externí odkaz: http://arxiv.org/abs/math/9204236

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