CFT 2011

Richard Borcherds constructed a lift from vector valued weakly holomorphic elliptic modular forms of weight $1-n/2$ to meromorphic modular forms for the discriminant kernel subgroup $\Gamma(L)$ of the orthogonal group of an even lattice $L$ of signature $(2,n)$. The forms in the image of the lift have their zeros and poles on Heegner divisors with known multiplicities. Since they have particular infinite product expansions, they are often called "Borcherds products". We consider a given meromorphic modular form $F$ for the group $\Gamma(L)$ whose zeros and poles lie on Heegner divisors. The converse theorem then states that, under certain assumptions on $L$, the form $F$ has to be the Borcherds lift of a weakly holomorphic modular form. We present some new results on this problem.

Montag, den 19. September 2011 um 11:00 Uhr, in INF288, HS2 Montag, den 19. September 2011 at 11:00, in INF288, HS2