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Presented By: Student Number Theory Seminar - Department of Mathematics

Student Number Theory: An introduction to Borcherds lifts

Beomseok Kwon

Let L be an even lattice of signature (2, n). The Borcherds lifting takes a weakly holomorphic modular form f for Mp(2, ℤ) of weight 1-n/2 valued in ℂ[L'/L] and produces a meromorphic modular form Ψ(f) for O⁺(L). The divisors of Borcherds lifts are supported on Heegner divisors. In fact, the weight and the divisor of Ψ(f) are completely determined by the constant term and the principal part of the Fourier expansion of f respectively. Furthermore, Borcherds lifts admit infinite product expansions known as Borcherds products. In this talk, we will use the regularized theta lifts of weak Maass forms to sketch the construction of Borcherds lifts.

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