MathVideos.org
  • Seminars
    • Algebra
      • Associative Rings
        • Ariki-Koike Algebras
        • Cluster Algebras
        • Group Rings
        • Hecke Algebras
        • KLR Algebras
        • Schur Algebras
      • Commutative Algebra
      • Fusion Systems
      • Group Theory
        • Abelian Groups
        • Algebraic Groups
        • Combinatorial Group Theory
        • Computational Group Theory
        • Finite Groups
        • Geometric Group Theory
        • Infinite Groups
        • Lie Groups
        • Permutation Groups
      • Lie Theory
        • Algebraic Groups
        • Lie Algebras
        • Lie Groups
        • p-Adic Groups
        • Representations of Algebraic Groups
      • Non-Associative Algebras
        • Jordan and Axial Algebras
        • Lie Algebras
        • Other Non-Associative Rings
      • Representation Theory
        • Geometric Representation Theory
        • Representations of Algebraic Groups
        • Representations of Finite Groups
        • Representations of Lie Algebras
        • Representations of Symmetric Groups
      • Semigroups
    • Analysis
      • Complex Analysis
      • Functional Analysis
      • Harmonic Analysis
    • Category Theory
      • Derived Categories
      • Higher Category Theory
      • Triangulated Categories
    • Combinatorics
      • Additive Combinatorics
      • Algebraic Combinatorics
      • Extremal Combinatorics
      • Graph Theory
    • Geometry
      • Algebraic Geometry
        • Birational Geometry
      • Differential Geometry
      • Discrete Geometry
      • Non-Commutative Geometry
      • Symplectic Geometry
    • Logic
    • Mathematical Finance
    • Mathematical Physics
    • Number Theory
      • Additive Number Theory
      • Analytic Number Theory
      • Algebraic Number Theory
      • Computational Number Theory
      • Diophantine Equations
      • Diophantine Geometry
      • Number Theory and Forms
      • Probabilistic Number Theory
    • Optimization
    • Probability Theory
    • Topology
      • Algebraic Topology
      • Analytic Topology
      • Differential Topology
      • Dynamical Systems
      • Geometric Topology
  • Short Courses
    • Algebra
    • Analysis
    • Category Theory
    • Combinatorics
    • Geometry
    • Mathematical Physics
    • Number Theory
    • Probability Theory
    • Topology
  • Lecture Courses
    • Algebra
    • Analysis
    • Category Theory
    • Combinatorics
    • Geometry
    • Mathematical Physics
    • Number Theory
    • Probability Theory
    • Topology
  • ···
    MathVideos.org
    • Seminars
      • Algebra
        • Associative Rings
          • Ariki-Koike Algebras
          • Cluster Algebras
          • Group Rings
          • Hecke Algebras
          • KLR Algebras
          • Schur Algebras
        • Commutative Algebra
        • Fusion Systems
        • Group Theory
          • Abelian Groups
          • Algebraic Groups
          • Combinatorial Group Theory
          • Computational Group Theory
          • Finite Groups
          • Geometric Group Theory
          • Infinite Groups
          • Lie Groups
          • Permutation Groups
        • Lie Theory
          • Algebraic Groups
          • Lie Algebras
          • Lie Groups
          • p-Adic Groups
          • Representations of Algebraic Groups
        • Non-Associative Algebras
          • Jordan and Axial Algebras
          • Lie Algebras
          • Other Non-Associative Rings
        • Representation Theory
          • Geometric Representation Theory
          • Representations of Algebraic Groups
          • Representations of Finite Groups
          • Representations of Lie Algebras
          • Representations of Symmetric Groups
        • Semigroups
      • Analysis
        • Complex Analysis
        • Functional Analysis
        • Harmonic Analysis
      • Category Theory
        • Derived Categories
        • Higher Category Theory
        • Triangulated Categories
      • Combinatorics
        • Additive Combinatorics
        • Algebraic Combinatorics
        • Extremal Combinatorics
        • Graph Theory
      • Geometry
        • Algebraic Geometry
          • Birational Geometry
        • Differential Geometry
        • Discrete Geometry
        • Non-Commutative Geometry
        • Symplectic Geometry
      • Logic
      • Mathematical Finance
      • Mathematical Physics
      • Number Theory
        • Additive Number Theory
        • Analytic Number Theory
        • Algebraic Number Theory
        • Computational Number Theory
        • Diophantine Equations
        • Diophantine Geometry
        • Number Theory and Forms
        • Probabilistic Number Theory
      • Optimization
      • Probability Theory
      • Topology
        • Algebraic Topology
        • Analytic Topology
        • Differential Topology
        • Dynamical Systems
        • Geometric Topology
    • Short Courses
      • Algebra
      • Analysis
      • Category Theory
      • Combinatorics
      • Geometry
      • Mathematical Physics
      • Number Theory
      • Probability Theory
      • Topology
    • Lecture Courses
      • Algebra
      • Analysis
      • Category Theory
      • Combinatorics
      • Geometry
      • Mathematical Physics
      • Number Theory
      • Probability Theory
      • Topology
    • ···
      MathVideos.org
      • Seminars
        • Algebra
          • Associative Rings
            • Ariki-Koike Algebras
            • Cluster Algebras
            • Group Rings
            • Hecke Algebras
            • KLR Algebras
            • Schur Algebras
          • Commutative Algebra
          • Fusion Systems
          • Group Theory
            • Abelian Groups
            • Algebraic Groups
            • Combinatorial Group Theory
            • Computational Group Theory
            • Finite Groups
            • Geometric Group Theory
            • Infinite Groups
            • Lie Groups
            • Permutation Groups
          • Lie Theory
            • Algebraic Groups
            • Lie Algebras
            • Lie Groups
            • p-Adic Groups
            • Representations of Algebraic Groups
          • Non-Associative Algebras
            • Jordan and Axial Algebras
            • Lie Algebras
            • Other Non-Associative Rings
          • Representation Theory
            • Geometric Representation Theory
            • Representations of Algebraic Groups
            • Representations of Finite Groups
            • Representations of Lie Algebras
            • Representations of Symmetric Groups
          • Semigroups
        • Analysis
          • Complex Analysis
          • Functional Analysis
          • Harmonic Analysis
        • Category Theory
          • Derived Categories
          • Higher Category Theory
          • Triangulated Categories
        • Combinatorics
          • Additive Combinatorics
          • Algebraic Combinatorics
          • Extremal Combinatorics
          • Graph Theory
        • Geometry
          • Algebraic Geometry
            • Birational Geometry
          • Differential Geometry
          • Discrete Geometry
          • Non-Commutative Geometry
          • Symplectic Geometry
        • Logic
        • Mathematical Finance
        • Mathematical Physics
        • Number Theory
          • Additive Number Theory
          • Analytic Number Theory
          • Algebraic Number Theory
          • Computational Number Theory
          • Diophantine Equations
          • Diophantine Geometry
          • Number Theory and Forms
          • Probabilistic Number Theory
        • Optimization
        • Probability Theory
        • Topology
          • Algebraic Topology
          • Analytic Topology
          • Differential Topology
          • Dynamical Systems
          • Geometric Topology
      • Short Courses
        • Algebra
        • Analysis
        • Category Theory
        • Combinatorics
        • Geometry
        • Mathematical Physics
        • Number Theory
        • Probability Theory
        • Topology
      • Lecture Courses
        • Algebra
        • Analysis
        • Category Theory
        • Combinatorics
        • Geometry
        • Mathematical Physics
        • Number Theory
        • Probability Theory
        • Topology
      Modular forms (Borcherds)

      Richard Borcherds: Modular forms, VII. Discriminant and E2

      26th March, 2021
      Watch LaterRemove Cinema Mode

      The previous lecture in this series is here. The next lecture in this series is here.

      We discuss the infinite product of the discriminant function and relate it to the fact that the Eisenstein series E2 is not quite a modular form. We then sketch Siegel’s proof of the infinite product for the discriminant.

      This video is part of a lecture course by Richard Borcherds from 2021.

      In This Lecture Course

      • Richard Borcherds: Modular forms, I. Introduction
      • Richard Borcherds: Modular forms, II. Eisenstein series
      • Richard Borcherds: Modular forms, III. Fourier coefficients of Eisenstein series
      • Richard Borcherds: Modular forms, IV. Fundamental domain
      • Richard Borcherds: Modular forms, V. Classification
      • Richard Borcherds: Modular forms, VI. Modular functions
      • Richard Borcherds: Modular forms, VII. Discriminant and E2
      • Richard Borcherds: Modular forms, VIII. Theta functions
      • Richard Borcherds: Modular forms, IX. Theta functions in higher dimensions
      • Richard Borcherds: Modular forms, X. Hecke operators
      • Richard Borcherds: Modular forms, XI. Product formula for j
      • Richard Borcherds: Modular forms, XII. Hecke operators for forms
      • Richard Borcherds: Modular forms, XIII. Petersson inner product

      In ‘Lecture Courses’

      • All Lecture Courses
      • Algebra
      • Analysis
      • Category Theory
      • Combinatorics
      • Geometry
      • Mathematical Physics
      • Number Theory
      • Probability Theory
      • Topology

      About MathVideos

      MathVideos attempts to produce a catalogue of all research-level seminar and course videos from across the Internet. Started by David Craven, it is not affiliated in any way with the University of Birmingham.

      Privacy Policy

      Contact Us

      Most recent videos

      • Nikolay Bogachev: Geometry, Arithmetic, and Dynamics of Discrete Groups, XXI 3rd December, 2024
      • David Fernández: Non-commutative Poisson geometry and pre-Calabi-Yau algebras 2nd December, 2024
      • Hadi Salmasian: Lie Groups and Quantization, XXIII 2nd December, 2024
      • Jon Woolf: Heart fans as universal phase diagrams 28th November, 2024
      • Nikolay Bogachev: Geometry, Arithmetic, and Dynamics of Discrete Groups, XX 28th November, 2024