منابع مشابه
Harmonic 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 Forms
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 b...
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...
متن کاملMOCK MODULAR FORMS AS p-ADIC MODULAR FORMS
In this paper, we consider the question of correcting mock modular forms in order to obtain p-adic modular forms. In certain cases we show that a mock modular form M is a p-adic modular form. Furthermore, we prove that otherwise the unique correction of M is intimately related to the shadow of M.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1986
ISSN: 0021-8693
DOI: 10.1016/0021-8693(86)90064-5