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Washington State University

Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar

Department of Mathematics and Statistics

Neill Hall 5W

October 15, Monday, 4:10 - 5:00 PM

Jakob Streipel

Department of Mathematics and Statistics

Washington State University

Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar

Department of Mathematics and Statistics

Neill Hall 5W

October 15, Monday, 4:10 - 5:00 PM

Jakob Streipel

Department of Mathematics and Statistics

Washington State University

Title: Special Relations Between Normalised Eisenstein Series

Abstract: We give an introduction to modular forms, cusp forms, and in particular (normalised) Eisenstein series $E_k$. We then go on to demonstrate that the well-known relations $E_4^2 = E_8$, $E_4 E_6 = E_{10}$, and $E_6 E_8 = E_4 E_{10} = E_{14}$ are the only relations of the form $E_k = E_l E_{k - l}$.

Abstract: We give an introduction to modular forms, cusp forms, and in particular (normalised) Eisenstein series $E_k$. We then go on to demonstrate that the well-known relations $E_4^2 = E_8$, $E_4 E_6 = E_{10}$, and $E_6 E_8 = E_4 E_{10} = E_{14}$ are the only relations of the form $E_k = E_l E_{k - l}$.