• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.1
• /
• pp.83-88
• /
• 2015

In this paper we give a determinant formula for the relative congruent zeta function in cyclotomic function fields.

• Communications of the Korean Mathematical Society
• /
• v.27 no.3
• /
• pp.455-464
• /
• 2012

In the previous paper [8], the author gave a determinant formula of relative zeta function for cyclotomic function fields. Our purpose of this paper is to extend this result for more general function fields. As an application of our formula, we will give determinant formulas of class numbers for constant field extensions.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.6
• /
• pp.1219-1224
• /
• 2011

In this paper we give a determinant formula for congruent zeta functions of real Abelian function fields. We also give some example of congruent zeta functions when the conductor of real Abelian function field is monic irreducible.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.1
• /
• pp.117-121
• /
• 2016

In this paper we give a determinant formula for the ratio of relative congruence zeta functions of cyclotomic function fields.

• Korean Journal of Mathematics
• /
• v.19 no.2
• /
• pp.129-147
• /
• 2011

In this paper we discuss the zeta-determinants of harmonic oscillators having general quadratic potentials defined on $\mathbb{R}^2$. By using change of variables we reduce the harmonic oscillators having general quadratic potentials to the standard harmonic oscillators and compute their spectra and eigenfunctions. We then discuss their zeta functions and zeta-determinants. In some special cases we compute the zeta-determinants of harmonic oscillators concretely by using the Riemann zeta function, Hurwitz zeta function and Gamma function.

• Journal of the Korean Mathematical Society
• /
• v.57 no.4
• /
• pp.1059-1059
• /
• 2020

• Honam Mathematical Journal
• /
• v.33 no.3
• /
• pp.321-333
• /
• 2011

During the last three decades, the problem of evaluation of the determinants of the Laplacians on Riemann manifolds has received considerable attention by many authors. The functional determinant for the n-dimensional sphere $S^n$ with the standard metric has been computed in several ways. Here we aim at computing the determinants of the Laplacians on $S^n$ (n = 8, 9) by mainly using ceratin known closed-form evaluations of series involving Zeta function.

• Journal of the Korean Mathematical Society
• /
• v.45 no.5
• /
• pp.1255-1274
• /
• 2008

The purpose of this paper is to discuss the constant term appearing in the BFK-gluing formula for the zeta-determinants of Laplacians on a complete Riemannian manifold when the warped product metric is given on a collar neighborhood of a cutting compact hypersurface. If the dimension of a hypersurface is odd, generally this constant is known to be zero. In this paper we describe this constant by using the heat kernel asymptotics and compute it explicitly when the dimension of a hypersurface is 2 and 4. As a byproduct we obtain some results for the value of relative zeta functions at s=0.

• Korean Journal of Mathematics
• /
• v.7 no.2
• /
• pp.159-166
• /
• 1999

For classical elliptic pseudodifferential operators $A({\lambda})$ of order $m$ > 0 with parameter ${\lambda}$ of weight ${\chi}$ > 0, it is known that $logDet_{\theta}A({\lambda})$ admits an asymptotic expansion as ${\theta}{\rightarrow}+{\infty}$. In this paper we show, with some assumptions, that the coefficients of ${\lambda}^-{\frac{n}{\chi}}$ can be expressed by the values of zeta functions at 0 for some elliptic ${\psi}$DO's on $M{\times}S^1{\times}{\cdots}{\times}S^1$ multiplied by $\frac{m}{c_{n-1}}$.