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FINITENESS THEOREMS FOR 2-UNIVERSAL HERMITIAN LATTICES OVER SOME IMAGINARY QUADRATIC FIELDS
박부성 영남수학회 2010 East Asian mathematical journal Vol.26 No.5
A positive definite Hermitian lattice is said to be 2-universal if it represents all positive definite binary Hermitian lattices. We find some finiteness theorems which ensure 2-universality of Hermitian lattices over several imaginary quadratic number fields.
Multiplicative functions which are additive on triangular numbers
박부성 대한수학회 2021 대한수학회보 Vol.58 No.3
Fix $k \ge 3$. If a multiplicative function $f$ satisfies \[ f(x_1+x_2+\dots+x_k) = f(x_1) + f(x_2) + \dots + f(x_k) \] for arbitrary positive triangular numbers $x_1, x_2, \dots, x_k$, then $f$ is the identity function. This extends Chung and Phong's work for $k=2$.