Modular forms: Fourier coefficients of Eisenstein series
This lecture is part of an online graduate course on modular forms. We calculate the Fourier coefficients of the Eisenstein series introduced in the previous lecture, and use them to construct the elliptic modular function. (Minor typo: in the definition of E10 I wrote 262 instead of 264.) For the other lectures in the course see • Modular forms

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Modular forms: Fundamental domain

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Modular forms: Eisenstein series

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Modular forms: Introduction

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The bridge between number theory and complex analysis

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We're 99.9% sure this pattern is true, but no one can prove it
![Kevin Buzzard (lecture 1/20) Automorphic Forms And The Langlands Program [2017]](https://i.ytimg.com/vi/Rv59aRUMfio/hqdefault.jpg?sqp=-oaymwEjCNACELwBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLCGc_eUm7mWd9-v1VMBlKy9vgjRmQ)
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Kevin Buzzard (lecture 1/20) Automorphic Forms And The Langlands Program [2017]

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Fourier Series Explained (for Beginners)

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Modular forms: Classification

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How Divergence and Curl Were Discovered

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Counting points on the E8 lattice with modular forms (theta functions) | #SoME2

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Elliptic functions lecture 3. Jacobi functions

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Elliptic functions 1. Weierstrass function.

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Modular forms: Theta functions

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Complex analysis: Singularities

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Modular forms: Modular functions

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Modular forms: Hecke operators

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But what is the Fourier Transform? A visual introduction.

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The Mathematical Problem with Music, and How to Solve It

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