منابع مشابه
Integrable systems and modular forms of level 2
A set of nonlinear differential equations associated with the Eisenstein series of the congruent subgroup Γ0(2) of the modular group SL2(Z) is constructed. These nonlinear equations are analogues of the well known Ramanujan equations, as well as the Chazy and Darboux-Halphen equations associated with the modular group. The general solutions of these equations can be realized in terms of the Sch...
متن کاملMulti-lagrangians for Integrable Systems
PACS numbers: 11.10.Ef 02.30.Wd 02.30.Jr 03.40.Gc Abstract We propose a general scheme to construct multiple Lagrangians for completely integrable non-linear evolution equations that admit multi-Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a conserved quantity higher/lower than the Hamiltonian in the potential part of the new Lagrangian and...
متن کاملHarmonic Maass Forms, Mock Modular Forms, and Quantum Modular Forms
This short course is an introduction to the theory of harmonic Maass forms, mock modular forms, and quantum modular forms. These objects have many applications: black holes, Donaldson invariants, partitions and q-series, modular forms, probability theory, singular moduli, Borcherds products, central values and derivatives of modular L-functions, generalized Gross-Zagier formulae, to name a few....
متن کاملModular Functions and Modular Forms
These are the notes for Math 678, University of Michigan, Fall 1990, exactly as they were handed out during the course except for some minor revisions and corrections. Please send comments and corrections to me at [email protected].
متن کاملSIEGEL MODULAR FORMS ( MOD p ) AND ALGEBRAIC MODULAR FORMS
In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → F̄p, where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre’s result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) o...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2010
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2010.02.006