Chang-Hwan Kim
Sungkyunkwan University · Mathematics
About the Lab
Professor Chang-Hwan Kim's research lab specializes in arithmetic geometry and automorphic forms, with a focus on modular forms, singular moduli, and Borcherds lifts. The lab investigates vector-valued modular forms, traces of singular moduli, and infinite product expansions related to Hauptmoduln, particularly in higher levels and genus zero cases. Key themes include the interplay between number theory and automorphic forms, especially through Zagier's trace formulas and the construction of explicit arithmetic invariants via modular lifting. The lab also explores the genus of congruence groups involving Fricke involutions, contributing to the classification of modular curves and their arithmetic properties.
Research Overview
Research Output Trend
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Selected Papers
15Let p be a prime for which the congruence group Γ0(p)* is of genus zero, and let 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 products associated to j p * and relate them to Zagier's trace formula for the singular values of j p * . 2000 Mat
We apply Zagier's result for the traces of singular moduli to construct Borcherds products in higher level cases.
Research Areas
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