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Orders at infinity of modular forms with Heegner divisors
2007
Proceedings of the American Mathematical Society
Borcherds described the exponents a(n) in product expansions n) of meromorphic modular forms with a Heegner divisor. His description does not directly give any information about h, the order of vanishing at infinity of f . We give p-adic formulas for h in terms of generalized traces given by sums over the zeroes and poles of f . Specializing to the case of the Hilbert class polynomial f = H d (j(z)) yields p-adic formulas for class numbers that generalize past results of Bruinier, Kohnen and
doi:10.1090/s0002-9939-07-08846-6
fatcat:6z2peot2q5gsxagit65rlbbf2e