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Chang Heon Kim

Publications and source records attributed to Chang Heon Kim.

21 records · Page 2Linked to original sources
arXiv2004

More on super-replication formulae

We extend Norton-Borcherds-Koike's replication formulae to super-replicable ones by working with the congruence groups $Γ_1(N)$ and find the product identities which characterize super-replicable functions. These will provide a clue for constructing certain new infinite dimensional Lie superalgebras whose denominator identities coincide with the above product identities. Therefore it could be one way to find a connection between modular functions and infinite dimensional Lie algebras.

math.NT↗
arXiv2003

Traces of singular values and Borcherds products

Let $p$ be a prime for which the congruence group $Γ_0(p)^*$ is of genus zero, and $j_p^*$ be the corresponding Hauptmodul. Let $f$ be a nearly holomorphic modular form of weight 1/2 on $Γ_0(4p)$ 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 products associated to $j_p^*$ and extend Zagier's trace formula for singular values of $j_p^*$. Further we investigate the twisted traces of sigular values of $j_p^*$ and construct Borcherds products related to them.

math.NT↗