Automorphic forms on O_{s+2,2}(R) and infinite products. 

Invent. Math. 120, p. 161-213 (1995) 

Richard E. Borcherds. 

Mathematics department, University of California at Berkeley, 
CA 94720-3840 U. S. A. 

18 August 1994, corrected 9 Dec. 



The denominator function of a generalized Kac-Moody 
algebra is often an automorphic form for the
group O_{s+2,2}(R) which can be written as an infinite 
product. We study such forms and construct some
infinite families of them. This has applications 
to the theory of generalized Kac-Moody algebras,
unimodular lattices, and reflection groups. We 
also use these forms to write several well known modular
forms, such as the elliptic modular function j and 
the Eisenstein series E_4 and E_6, as infinite products.