Towards finite-gap integration of the Inozemtsev model.
Takemura, Kouichi (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Displaying similar documents to “From holonomy of the Ising model form factors to -fold integrals and the theory of elliptic curves.”
Towards finite-gap integration of the Inozemtsev model.
Quasi-modular forms attached to elliptic curves, I
Hossein Movasati (2012)
Annales mathématiques Blaise Pascal
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In the present text we give a geometric interpretation of quasi-modular forms using moduli of elliptic curves with marked elements in their de Rham cohomologies. In this way differential equations of modular and quasi-modular forms are interpreted as vector fields on such moduli spaces and they can be calculated from the Gauss-Manin connection of the corresponding universal family of elliptic curves. For the full modular group such a differential equation is calculated and it turns out...
Differential and functional identities for the elliptic trilogarithm.
Strachan, Ian A.B. (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Computing Gauss-Manin systems for complete intersection singularities .
Aleksandrov, A.G., Tanabé, S. (1996)
Georgian Mathematical Journal
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A remark on Nilsson type integrals
Nguyen Minh, Bogdan Ziemian (1996)
Banach Center Publications
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We investigate ramification properties with respect to parameters of integrals (distributions) of a class of singular functions over an unbounded cycle which may intersect the singularities of the integrand. We generalize the classical result of Nilsson dealing with the case where the cycle is bounded and contained in the set of holomorphy of the integrand. Such problems arise naturally in the study of exponential representation at infinity of solutions to certain PDE's (see [Z]). ...
Spectral curves of operators with elliptic coefficients.
Eilbeck, J.Chris, Enolski, Victor Z., Previato, Emma (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Integrable models of interaction of matter with radiation.
Inozemtsev, Vladimir I., Inozemtseva, Natalia G. (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Bethe ansatz for the Ruijsenaars model of -type.
Chalykh, Oleg (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Quasi-exactly solvable -body spin Hamiltonians with short-range interaction potentials.
Enciso, A, Finkel, F., González-López, A., Rodríguez, M.A. (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Gravity, strings, modular and quasimodular forms
P. Marios Petropoulos, Pierre Vanhove (2012)
Annales mathématiques Blaise Pascal
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Modular and quasimodular forms have played an important role in gravity and string theory. Eisenstein series have appeared systematically in the determination of spectrums and partition functions, in the description of non-perturbative effects, in higher-order corrections of scalar-field spaces, ...The latter often appear as gravitational instantons as special solutions of Einstein’s equations. In the present lecture notes we present a class of such solutions in four dimensions, obtained...