Elliptic Curves and Modular Forms
نویسنده
چکیده
This is an exposition of some of the main features of the theory of elliptic curves and modular forms.
منابع مشابه
Topics in Elliptic Curves and Modular Forms
This is an exposition of some of the main features of the theory of elliptic curves and modular forms.
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The cohomology theory known as Tmf, for “topological modular forms,” is a universal object mapping out to elliptic cohomology theories, and its coefficient ring is closely connected to the classical ring of modular forms. We extend this to a functorial family of objects corresponding to elliptic curves with level structure and modular forms on them. Along the way, we produce a natural way to re...
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1 SL2(Z) and elliptic curves 2 1.1 SL2(Z) and the moduli of complex tori . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 The Fundamental region and a system of generators . . . . . . . . . . . . . . . . . . . . . 3 1.3 The Weierstrass ℘ function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Nonsingular cubics and the invariant j . . . . . . . . . . . ...
متن کاملASPECTS OF COMPLEX MULTIPLICATION Contents
1. Preview 2 Complex multiplication on elliptic curves over C 2 Traces of singular moduli 3 Class field theory 3 The Kronecker limit formula and Kronecker’s solution of Pell’s equation 4 Application to Diophantine equations (Villegas) 4 L-series and CM modular forms 5 Other topics 6 2. Complex Multiplication on Elliptic Curves over C 6 Elliptic Curves over C 6 Elliptic functions 7 Complex multi...
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The p-adic interpolation of modular forms on congruence subgroups of SL2(Z) has been succesfully used in the past to interpolate values of L-series. In [12], Serre interpolated the values at negative integers of the ζ-series of a totally real number field (in fact of L-series of powers of the Teichmuller character) by interpolating Eisenstein series, which are holomorphic modular forms, and loo...
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