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$𝒟$ -bundles and integrable hierarchies

David Ben-Zvi, Thomas Nevins (2011)

Journal of the European Mathematical Society

We study the geometry of $𝒟$ -bundles—locally projective $𝒟$ -modules—on algebraic curves, and apply them to the study of integrable hierarchies, specifically the multicomponent Kadomtsev–Petviashvili (KP) and spin Calogero–Moser (CM) hierarchies. We show that KP hierarchies have a geometric description as flows on moduli spaces of $𝒟$ -bundles; in particular, we prove that the local structure of $𝒟$ -bundles is captured by the full Sato Grassmannian. The rational, trigonometric, and elliptic solutions of KP...

2-torsion of the Brauer group of an elliptic curve: Generators and relations.

Chernousov, V., Guletskiĭ, V. (2001)

Documenta Mathematica

A characterization of integral elliptic automorphic forms

Andrea Mori (1994)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

A class of diophantine equations connected with certain elliptic curves over $Q (\sqrt{- 13})$

R. J. Stroeker (1979)

Compositio Mathematica

A concept of Bernoulli numbers in algebraic function fields.

Chip Snyder (1979)

Journal für die reine und angewandte Mathematik

A diophantine system.

Bremner, Andrew (1986)

International Journal of Mathematics and Mathematical Sciences

A finiteness theorem for the symmetric square of an elliptic curve.

Matthias Flach (1992)

Inventiones mathematicae

A functional equation originating from elliptic curves.

Park, Won-Gil, Bae, Jae-Hyeong (2008)

Abstract and Applied Analysis

A generalization of the Chowla-Selberg formula.

Y. Nakkajima, Y. Taguchi (1991)

Journal für die reine und angewandte Mathematik

A Lax formalism for the elliptic difference Painlevé equation.

Yamada, Yasuhiko (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

A new construction of $p$ -adic $L$ -functions attached to certain elliptic curves with complex multiplication

John L. Boxall (1986)

Annales de l'institut Fourier

In this paper we apply the results of our previous article on the $p$ -adic interpolation of logarithmic derivatives of formal groups to the construction of $p$ -adic $L$ -functions attached to certain elliptic curves with complex multiplication. Our results are primarily concerned with curves with supersingular reduction.

A new cubic character sum

A. Rajwade, J. Parnami (1982)

Acta Arithmetica

A note on elliptic curves over finite fields

J.F. Voloch (1988)

Bulletin de la Société Mathématique de France

A note on linear preserves of ternary cubic forms

Agnieszka Chlebowicz, Małgorzata Wołowiec-Musiał (2001)

Acta Mathematica et Informatica Universitatis Ostraviensis

A note on Weierstrass Points of Bielliptic curves.

Jihun Park (1998)

Manuscripta mathematica

À propos de la conjecture de Manin pour les courbes elliptiques modulaires

Ahmed Abbes, Emmanuel Ullmo (1996)

Compositio Mathematica

A remark about isogenies of elliptic curves over quadratic fields

Gerhard Frey (1986)

Compositio Mathematica

A remark on a theorem of Chowla-Cowles.

Hideji Ito (1982)

Journal für die reine und angewandte Mathematik

A Remark on the Sato-Tate Conjecture.

A.P. OGG (1969/1970)

Inventiones mathematicae

Abelian surfaces and products of elliptic curves

Marina Rosanna Marchisio (1998)

Bollettino dell'Unione Matematica Italiana

Si dà una nuova e completa dimostrazione del risultato cruciale del metodo di Ruppert che consente di stabilire in maniera effettiva quando una superficie abeliana è isomorfa o isogena a un prodotto di curve ellittiche.

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