• 대한수학회논문집
• /
• 제20권2호
• /
• pp.247-257
• /
• 2005

In this paper we calculate two special types of multiple zeta values, $\zeta(\{4\iota+2\}_n)\;and\;\zeta(\{4\iota\}_n)$ using the primitive roots of unity, which may be simpler and easier.

• East Asian mathematical journal
• /
• 제18권2호
• /
• pp.219-224
• /
• 2002

Recently the theory of the multiple Gamma functions, which were studied by Barnes and others a century ago, has been revived in the study of determinants of Laplacians. Here we are aiming at evaluating the values of the multiple Gamma functions ${\Gamma}_n(\frac{1}{2})$ in terms of the Hurwitz or Riemann Zeta functions.

• 대한수학회보
• /
• 제58권5호
• /
• pp.1261-1278
• /
• 2021

Recently, a new kind of multiple zeta value of level two T(k) (which is called multiple T-value) was introduced and studied by Kaneko and Tsumura. In this paper, we define a kind of alternating version of multiple T-values, and study several duality formulas of weighted sum formulas about alternating multiple T-values by using the methods of iterated integral representations and series representations. Some special values of alternating multiple T-values can also be obtained.

• 대한수학회보
• /
• 제49권1호
• /
• pp.165-174
• /
• 2012

In this paper, we construct a p-adic analogue of multiple Riemann zeta values and express their values at non-positive integers. In particular, we obtain a new congruence of the higher order Frobenius-Euler numbers and the Kummer congruences for the Bernoulli numbers as a corollary.

• 대한수학회지
• /
• 제55권5호
• /
• pp.1207-1220
• /
• 2018

The generalized hyperharmonic numbers $h^{(m)}_n(k)$ are defined by means of the multiple harmonic numbers. We show that the hyperharmonic numbers $h^{(m)}_n(k)$ satisfy certain recurrence relation which allow us to write them in terms of classical harmonic numbers. Moreover, we prove that the Euler-type sums with hyperharmonic numbers: $$S(k,m;p):=\sum\limits_{n=1}^{{\infty}}\frac{h^{(m)}_n(k)}{n^p}(p{\geq}m+1,\;k=1,2,3)$$ can be expressed as a rational linear combination of products of Riemann zeta values and harmonic numbers. This is an extension of the results of Dil [10] and $Mez{\ddot{o}}$ [19]. Some interesting new consequences and illustrative examples are considered.