p-adic analysis of algebraic numer fields and algorithm on algebraic number fields or finite fields

A. Kudo研究了计算伯努利数的p进性质的算法，整数的质因数分解和卡迈克尔数的计算。证明了p进zeta函数的p进欧拉常数γ_p对于模p （p【大于等于】5）等于-(B_<p-1>/(p-1) -1 /p)，其中B_n表示第n个伯努利数，并计算了它们在p【小于等于】20,000,000时的值（modp）。推导出在p≠5,13,563的范围内γ_p*0 （modp）。他还用质因数分解法计算了所有小于10^<17>的卡迈克尔数。Washio研究了有限域上椭圆曲线的类数和Hasse不变量。通过确定有理点的个数，得到了有限素域GF(p)上椭圆曲线超奇异的充分条件，并给出了新的二项式系数等式。Sueyoshi研究了有限域GF(2)上二次数域和矩阵的4类秩。利用Redei矩阵，证明了二次数域的窄4类秩之间的新的不等式关系。他进一步给出了具有最小秩的Redei矩阵的一个表征。作为这些结果的应用，他还证明了如果虚二次数域K的理想类群包含类型为（4,4,2,2）的子群，且4不包含在K的素数判别式中，则K的2类域塔是无穷大的。Maruyama用有限自动机理论研究离散优化问题。他提出了一种新的序列决策过程的概念，称为双元序列决策过程，并给出了离散决策过程的强表示定理。

A. Kudo studied algorithms for computing p-adic properties of Bernoulli numbers, for prime factor ization of integers and for calculation of Carmichael numbers. He proved that the p-adic Euler constant γ_p of p-adic zeta function is equivalent to -(B_<p-1>/(p-1) - 1/p) for modulo p (p【greater than or equal】5), where B_n denotes the n-th Bernoulli number, and calculated the value (modp) of them for p【less than or equal】20,000,000. It is derived that in this range γ_p*0 (modp) for p≠5, 13, 563. Also he calculated all Carmichael numbers less than 10^<17> with their prime factorizations.T. Washio studied class number and Hasse invariants of elliptic curves over finite fields. By means of determination of the number of rational points, he derived a sufficient condition for an elliptic curve over a finite prime field GF(p) to be supersingular, and gave a new equality of binomial coefficients.Y. Sueyoshi studied 4-class ranks of quadratic number fields and matrices over finite field GF(2). Using Redei matrices, he proved new inequality relations between the narrow 4-class ranks of quadratic number fields. He further gave a characterization of Redei matrices with minimal rank. As an application of these results, he also proved the fact that if the ideal class group of imaginary quadratic number field K contains a subgroup of type (4,4, 2,2) and 4 is not contained in the prime discriminant of K, then the 2-class field tower of K is infinite.Y. Maruyama studied discrete optimization problems using the theory of finite automata. He intro duced the notion of a new sequential decision process called bitone sequential decision process and gave a strong representation theorem for a discrete decision process.