배성한 교수

Abstract We study the genus theory for function fields which is the analogue of the classical genus theory developed by Hasse and Fröhlich.

Some interesting properties of Carlitz cyclotomic polynomials analogous to those of classical cyclotomic polynomials are given.

We investigate algebraic \Gamma-monomials of Thakur's positive characteristic \Gamma-function, by using Anderson-Das double complex method of computing the sign-cohomology of the universal ordinary distribution. We prove that the \Gamma-monomial associated to an element of the second sign-cohomology of the universal ordinary distribution of \mathbb{F}_{q}(T) generates a Kummer extension of the Carlitz cyclotomic function field, which is also a Galois extension of

We determine all real quadratic function fields of Richaud-Degert type with ideal class number one.

We investigate algebraic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Gamma"> <mml:semantics> <mml:mi mathvariant="normal"> Γ </mml:mi> <mml:annotation encoding="application/x-tex">\Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -monomials of Thakur’s positive characteristic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper