Notes on Borcherds Products
نویسنده
چکیده
These are the notes for a short course on Borcherds Products held in Aachen on 1st2nd August 2012. The lectures are intended for someone who does not know what a Borcherds product is, but does know what a modular form is. In preparing these notes I’ve used the following sources: [1, 2, 3, 4, 5]. All the correct statements in these notes are taken from those sources, and all the mistakes are my own.
منابع مشابه
Zagier Duality for the Exponents of Borcherds Products for Hilbert Modular Forms
A certain sequence of weight 1/2 modular forms arises in the theory of Borcherds products for modular forms for SL2(Z). Zagier proved a family of identities between the coefficients of these weight 1/2 forms and a similar sequence of weight 3/2 modular forms, which interpolate traces of singular moduli. We obtain the analogous results for modular forms arising from Borcherds products for Hilber...
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Abstract. Let p be a prime for which the congruence group Γ0(p) ∗ is of genus zero, and j∗ p be the corresponding Hauptmodul. Let f be a nearly holomorphic modular form of weight 1/2 on Γ0(4p) which satisfies some congruence condition on its Fourier coefficients. We interpret f as a vector valued modular form. Applying Borcherds lifting of vector valued modular forms we construct infinite produ...
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