http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
INTEGRAL BASES OVER p-ADIC FIELDS
Zaharescu, Alexandru Korean Mathematical Society 2003 대한수학회보 Vol.40 No.3
Let p be a prime number, $Q_{p}$ the field of p-adic numbers, K a finite extension of $Q_{p}$, $\bar{K}}$ a fixed algebraic closure of K and $C_{p}$ the completion of K with respect to the p-adic valuation. Let E be a closed subfield of $C_{p}$, containing K. Given elements $t_1$...,$t_{r}$ $\in$ E for which the field K($t_1$...,$t_{r}$) is dense in E, we construct integral bases of E over K.
Integral bases over $p$-adic fields
Alexandru Zaharescu 대한수학회 2003 대한수학회보 Vol.40 No.3
Let p be a prime number, Q_p the field of p-adic numbers,K a finite extension of Q_p, bar K a fixed algebraicclosure of K and C_p the completion of bar K with respectto the p-adic valuation. Let E be a closed subfield of C_p,containing K. Given elements t_1,dots ,t_rin E for which thefield K(t_1,dots,t_r) is dense in E, we construct integralbases of E over K.
A CLASS OF ARITHMETIC FUNCTIONS ON PSL<sub>2</sub>(ℤ), II
Spiegelhalter, Paul,Zaharescu, Alexandru Korean Mathematical Society 2014 대한수학회보 Vol.51 No.2
Atanassov introduced the irrational factor function and the strong restrictive factor function, which he defined as $I(n)=\displaystyle\prod_{p^{\alpha}||n}^{}p^{1/{\alpha}}$ and $R(n)=\displaystyle\prod_{p^{\alpha}||n}^{}p^{{\alpha}-1}$ in [2] and [3]. Various properties of these functions have been investigated by Alkan, Ledoan, Panaitopol, and the authors. In the prequel, we expanded these functions to a class of elements of $PSL_2(\mathbb{Z})$, and studied some of the properties of these maps. In the present paper we generalize the previous work by introducing real moments and considering a larger class of maps. This allows us to explore new properties of these arithmetic functions.
A MULTIVARIABLE MAYER-ERDÖS PHENOMENON
Meng, Xianchang,Zaharescu, Alexandru Korean Mathematical Society 2014 대한수학회지 Vol.51 No.5
In this paper we consider a generalization of the Mayer-Erd$\ddot{o}$s phenomenon discussed in [12] to linear forms in a larger number of variables.
A CLASS OF ARITHMETIC FUNCTIONS ON PSL<sub>2</sub>(Z)
Spiegelhalter, Paul,Zaharescu, Alexandru Korean Mathematical Society 2013 대한수학회보 Vol.50 No.2
In [3] and [2], Atanassov introduced the two arithmetic functions $$I(n)=\prod_{p^{\alpha}{\parallel}n}\;p^{1/{\alpha}}\;and\;R(n)=\prod_{p^{\alpha}{\parallel}n}\;p^{{\alpha}-1}$$ called the irrational factor and the restrictive factor, respectively. Alkan, Ledoan, Panaitopol, and the authors explore properties of these arithmetic functions in [1], [7], [8] and [9]. In the present paper, we generalize these functions to a larger class of elements of $PSL_2(\mathbb{Z})$, and explore some of the properties of these maps.
A CLASS OF EXPONENTIAL CONGRUENCES IN SEVERAL VARIABLES
Choi, Geum-Lan,Zaharescu, Alexandru Korean Mathematical Society 2004 대한수학회지 Vol.41 No.4
A problem raised by Selfridge and solved by Pomerance asks to find the pairs (a, b) of natural numbers for which $2^a\;-\;2^b$ divides $n^a\;-\;n^b$ for all integers n. Vajaitu and one of the authors have obtained a generalization which concerns elements ${\alpha}_1,\;{\cdots},\;{{\alpha}_{\kappa}}\;and\;{\beta}$ in the ring of integers A of a number field for which ${\Sigma{\kappa}{i=1}}{\alpha}_i{\beta}^{{\alpha}i}\;divides\;{\Sigma{\kappa}{i=1}}{\alpha}_i{z^{{\alpha}i}}\;for\;any\;z\;{\in}\;A$. Here we obtain a further generalization, proving the corresponding finiteness results in a multidimensional setting.
STRONG AND WEAK ATANASSOV PAIRS
P. SPIEGELHALTER,A. Zaharescu 장전수학회 2011 Proceedings of the Jangjeon mathematical society Vol.14 No.3
We study the irrational factor I(n) and the restrictive factor R(n) introduced by Atanassov and defined by I(n) = [수식],where [수식] is the prime factorization of n. We consider weighted combinations I(n)^aR(n)^b and characterize the pairs (a,b) in order to measure how close n is to being k-power full or k-power free. We also establish an asymptotic formula for weighted averages of the function I(n)^aR(n)^b.
A CLASS OF ARITHMETIC FUNCTIONS ON PSL2(Z), II
Paul Spiegelhalter,Alexandru Zaharescu 대한수학회 2014 대한수학회보 Vol.51 No.2
Atanassov introduced the irrational factor function and the strong restrictive factor function, which he dened as I(n) = Y pα∥n p1=α and R(n) = Y pα∥n pα-1 in [2] and [3]. Various properties of these functions have been investi- gated by Alkan, Ledoan, Panaitopol, and the authors. In the prequel, we expanded these functions to a class of elements of PSL2(Z), and studied some of the properties of these maps. In the present paper we generalize the previous work by introducing real moments and considering a larger class of maps. This allows us to explore new properties of these arithmetic functions.
A MULTIVARIABLE MAYER-ERD ¨ OS PHENOMENON
Xianchang Meng,Alexandru Zaharescu 대한수학회 2014 대한수학회지 Vol.51 No.5
In this paper we consider a generalization of the Mayer-Erdös phenomenon discussed in [12] to linear forms in a larger number of vari- ables.
A class of arithmetic functions on PSL2(Z)
Paul Spiegelhalter,Alexandru Zaharescu 대한수학회 2013 대한수학회보 Vol.50 No.2
In [3] and [2], Atanassov introduced the two arithmetic func- tions [수식] called the irrational factor and the restrictive factor, respectively. Alkan, Ledoan, Panaitopol, and the authors explore properties of these arith- metic functions in [1], [7], [8] and [9]. In the present paper, we generalize these functions to a larger class of elements of PSL2(Z), and explore some of the properties of these maps.