http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
ON THE CONVOLUTION SUMS OF CERTAIN RESTRICTED DIVISOR FUNCTIONS
( Dae Yeoul Kim ),( Aeran Kim ),( Sankaranarayanan ),( Ayyadurai ) 호남수학회 2013 호남수학학술지 Vol.35 No.2
We study convolution sums of certain restricted divisor functions in detail and present explicit evaluations in terms of usual divisor functions for some specific situations.
ON THE INFINITE PRODUCTS DERIVED FROM THETA SERIES II
Kim, Dae-Yeoul,Koo, Ja-Kyung Korean Mathematical Society 2008 대한수학회지 Vol.45 No.5
Let k be an imaginary quadratic field, ${\eta}$ the complex upper half plane, and let ${\tau}{\in}{\eta}{\cap}k,\;q=e^{{\pi}{i}{\tau}}$. For n, t ${\in}{\mathbb{Z}}^+$ with $1{\leq}t{\leq}n-1$, set n=${\delta}{\cdot}2^{\iota}$(${\delta}$=2, 3, 5, 7, 9, 13, 15) with ${\iota}{\geq}0$ integer. Then we show that $q{\frac}{n}{12}-{\frac}{t}{2}+{\frac}{t^2}{2n}{\prod}_{m=1}^{\infty}(1-q^{nm-t})(1-q^{{nm}-(n-t)})$ are algebraic numbers.
ON THE INFINITE PRODUCTS DERIVED FROM THETA SERIES I
Kim, Dae-Yeoul,Koo, Ja-Kyung Korean Mathematical Society 2007 대한수학회지 Vol.44 No.1
Let k be an imaginary quadratic field, h the complex upper half plane, and let $\tau{\in}h{\cap}k,\;q=e^{{\pi}i\tau}$. In this article, we obtain algebraic numbers from the 130 identities of Rogers-Ramanujan continued fractions investigated in [28] and [29] by using Berndt's idea ([3]). Using this, we get special transcendental numbers. For example, $\frac{q^{1/8}}{1}+\frac{-q}{1+q}+\frac{-q^2}{1+q^2}+\cdots$ ([1]) is transcendental.
A Remark Of P(i,k) On Elliptic Curves And Application For Manchester Coding
( Dae Yeoul Kim ),( Min Soo Kim ) 호남수학회 2011 호남수학학술지 Vol.33 No.2
Greg([Greg]) considered that N(k)=(k)∑(i=1)(-1)(i+1)(P(i,k))(P)N1, Where the P(i,k)`s were polynomials with possitive integer coefficients.In this paper, we will give the equations for ∑P(i,k) modulo 3. Usingthis, if we send a information for elliptic curve to sender, we canmake a new checksum method for Manchester coding in IEEE 802.3or IEEE 802.4.
ARITHMETIC OF INFINITE PRODUCTS AND ROGERS-RAMANUJAN CONTINUED FRACTIONS
Kim, Dae-Yeoul,Koo, Ja-Kyung,Simsek, Yilmaz Korean Mathematical Society 2007 대한수학회논문집 Vol.22 No.3
Let k be an imaginary quadratic field, h the complex upper half plane, and let $\tau{\in}h{\cap}k$, $q=e^{{\pi}i\tau}$. We find a lot of algebraic properties derived from theta functions, and by using this we explore some new algebraic numbers from Rogers-Ramanujan continued fractions.
Convolution Sum ∑(m<n/8)/σ1(2m)σ1(n-8m)
( Dae Yeoul Kim ),( Ae Ran Kim ),( Hwa Sin Park ) 호남수학회 2012 호남수학학술지 Vol.34 No.1
In this paper, we present the convolution sum ∑(m<n/8)/ σ1(2m)σ1(n-8m) evaluated for all n □ N.
ONVOLUTION SUM Σ<sub>m</sub><sub><</sub><sub>n/8</sub>σ<sub>1</sub>(2m)σ<sub>1</sub>(n-8m)
Kim, Dae-Yeoul,Kim, Ae-Ran,Park, Hwa-Sin The Honam Mathematical Society 2012 호남수학학술지 Vol.34 No.1
In this paper, we present the convolution sum ${\sum}_{m<n/8}{\sigma}_1(2m){\sigma}_1(n-8m)$ evaluated for all $n{\in}\mathbb{N}$.
ALGEBRAIC NUMBERS, TRANSCENDENTAL NUMBERS AND ELLIPTIC CURVES DERIVED FROM INFINITE PRODUCTS
Kim, Dae-Yeoul,Koo, Ja-Kyung Korean Mathematical Society 2003 대한수학회지 Vol.40 No.6
Let k be an imaginary quadratic field, η the complex upper half plane, and let $\tau$ $\in$ η $textsc{k}$, p = $e^{{\pi}i{\tau}}$. In this article, using the infinite product formulas for g2 and g3, we prove that values of certain infinite products are transcendental whenever $\tau$ are imaginary quadratic. And we derive analogous results of Berndt-Chan-Zhang ([4]). Also we find the values of (equation omitted) when we know j($\tau$). And we construct an elliptic curve E : $y^2$ = $x^3$ + 3 $x^2$ + {3-(j/256)}x + 1 with j = j($\tau$) $\neq$ 0 and P = (equation omitted) $\in$ E.
Combinatoric Convolution Sums Containing σ and ð of the Form 2m p
( Dae Yeoul Kim ),( Joong Soo Park ) 호남수학회 2014 호남수학학술지 Vol.36 No.3
In this paper, we study combinatoric convolution sums of divisor functions and get values of this sum when n=2m p. We find that the value of this convolution sum is represented by a sum of powers of 2 and Bernoulli or Euler number.