Modular Forms
نویسنده
چکیده
Here are the notes I took for Wei Zhang’s course on modular forms offered at Columbia University in Spring 2013 (MATH G4657: Algebraic Number Theory). Hopefully these notes will appear in a more complete form during Fall 2014. I recommend that you visit my website from time to time for the most updated version. Due to my own lack of understanding of the materials, I have inevitably introduced both mathematical and typographical errors in these notes. Please send corrections and comments to [email protected].
منابع مشابه
On the Jacquet–Langlands correspondence for Hilbert modular forms
2 Modular forms and Automorphic forms 2 2.1 Modular Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 The Adele group of GL2 over Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Automorphic Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Hecke act...
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A certain sequence of weight 1/2 modular forms arises in the theory of Borcherds products for modular forms for SL2(Z). Zagier proved a family of identities between the coefficients of these weight 1/2 forms and a similar sequence of weight 3/2 modular forms, which interpolate traces of singular moduli. We obtain the analogous results for modular forms arising from Borcherds products for Hilber...
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We explain how weight-two modular forms on 0.N / are related to modular symbols, and how to use this to explicitly compute spaces of modular forms.
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In this thesis, we set up the basic theory of p-adic modular forms over Shimura curves over Q, parallel to the classical case over modular curves. We define and study the structure of the spaces of p-adic modular forms with respect to certain quaternion algebras over Q. We study the relation of these modular forms with classical quaternionic modular forms. We prove a canonical subgroup theorem ...
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تاریخ انتشار 2014