SiC56327

2003-2022 全部

XIN Guoce,ZHOU Yue

We give a Laurent series proof of the Habsieger-Kadell q-Morris identity, which is a common generalization of the q-Morris Identity and the Aomoto constant term identity.

2013-03-08

Specialized Research Fund for the Doctoral Program of Higher Education（20110162120074

Department of mathematics, Capital Normal University, Beijing 100048 ,School of Mathematics and Statistics, Central South University, Changsha 410075

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Fu-Gao SONG

All sieve methods for the Goldbach problem sift out all the composite numbers; even though, strictly speaking, it is not necessary to do so. Furthermore, the sifting out of all composite numbers is, in general, very difficult. A new method introduced in this paper shows that the Goldbach problem can be solved by using a combination of algebraic techniques and existing results from sieve theory under sifting out only some composite numbers. In fact, in order to prove the Goldbach conjecture, it is only necessary to show that there are prime numbers left in the residual integers after the initial sifting! This idea can be implemented by using a method called “sifting function partition by integer sort”. Under this scheme, the integers are first classified according to their number of prime divisors; the sifting functions are then partitioned according to integer sort; the total number of integers in each class (containing the class of prime) is then determined by using the method of “separation of variables”; and the Goldbach conjecture is proved. This is a feasible method for solving both the Goldbach problem and the problem of twin primes. An added bonus of the above scheme is the elimination of the indeterminacy of the sifting functions brought about by their upper and lower bounds.

2006-04-04

College of Science, Shenzhen University

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Fu-Gao SONG

The term “Proposition {1, b}” means that every large even number N can be expressed as the sum of a prime and the product of at most b primes. All sieve methods for the Goldbach problem sift out all the composite numbers; even though, strictly speaking, it is not necessary to do so. Furthermore, the sifting out of all composite numbers is, in general, very difficult. This paper shows that Proposition {1, 1} will be solved if only Proposition {1, b} is proved. In fact, there are a large number of primes in the residual integers of Proposition {1, b} after sifting, of which all those integers not exceeding N^(2/(1+b)) are primes. Therefore, as long as these primes that do not exceed N^(2/(1+b)) can be separated from the residual integers and that their total number can be proved to be greater than zero, Proposition {1, 1} will be true. This idea can be implemented by using a method called “the sifting function partition by intervals”. This is a feasible method for solving both the Goldbach problem and the problem of twin primes. An added bonus of the above scheme is the elimination of the indeterminacy of the sifting functions brought about by their upper and lower bounds.

2006-04-05

College of Science, Shenzhen University

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2005-09-12

{1, 1}. 这一想法可以用分割筛法实现. 第二种方法是整数分类筛法. 该法根据素因子个数对整数进行分类，然后用Selberg筛法和“分离变量法”确定每一类整数的个数，其中素数个数自然得以确定

#数学#

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Fu-Gao SONG

Goldbach problem can be solved by using “the comparative sieve method”, in which a set of integers and its compared subset will be sifted simultaneously. By comparing the difference between the sifting function and the compared sifting function we can prove that there must be a large number of primes in the sifting function; this fact already enough proves the correctness of both the Goldbach problem and the problem of twin primes. On an added bonus, the indeterminacy of the sifting functions brought about by their upper and lower bounds can be eliminated, thereout, we can further obtain the first approximations for both problems.

2006-04-03

College of Science, Shenzhen University

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