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Exceptional modular form of weight 4 on an exceptional domain contained in C.

Henry H. Kim — 1993

Revista Matemática Iberoamericana

Resnikoff [12] proved that weights of a non trivial singular modular form should be integral multiples of 1/2, 1, 2, 4 for the Siegel, Hermitian, quaternion and exceptional cases, respectively. The θ-functions in the Siegel, Hermitian and quaternion cases provide examples of singular modular forms (Krieg [10]). Shimura [15] obtained a modular form of half-integral weight by analytically continuing an Eisenstein series. Bump and Bailey suggested the possibility of applying an analogue of Shimura's...

Dihedral and cyclic extensions with large class numbers

Peter J. ChoHenry H. Kim — 2012

Journal de Théorie des Nombres de Bordeaux

This paper is a continuation of []. We construct unconditionally several families of number fields with large class numbers. They are number fields whose Galois closures have as the Galois groups, dihedral groups D n , n = 3 , 4 , 5 , and cyclic groups C n , n = 4 , 5 , 6 . We first construct families of number fields with small regulators, and by using the strong Artin conjecture and applying some modification of zero density result of Kowalski-Michel, we choose subfamilies such that the corresponding L -functions are zero free...

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