The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 2-dimensional Kloostermann sums mod p, and ...The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 2-dimensional Kloostermann sums mod p, and give an exact computational formula for it.展开更多
The main purpose of this paper is using the analytic methods, the solutions of the congruence equation mod p and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the gen...The main purpose of this paper is using the analytic methods, the solutions of the congruence equation mod p and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 3-dimensional Kloostermann sums mod p, and give a sharp asymptotic formula for it.展开更多
The main purpose of this paper is, using the analytic method, to study the mean value properties of the complete trigonometric sums with Dirichlet characters, and give an exact calculating formula for its fourth power...The main purpose of this paper is, using the analytic method, to study the mean value properties of the complete trigonometric sums with Dirichlet characters, and give an exact calculating formula for its fourth power mean.展开更多
In 1923, Hardy and Littlewood[1] conjectured that each integer n can be written asp+m12+ m22 = n,and Linnik[2,3] proved that this conjecture is true. But if these mi with i = 1,2 are restricted to primes Pi, the corre...In 1923, Hardy and Littlewood[1] conjectured that each integer n can be written asp+m12+ m22 = n,and Linnik[2,3] proved that this conjecture is true. But if these mi with i = 1,2 are restricted to primes Pi, the corresponding result is out of reach at present. We consider the following Diophantine equation展开更多
Let q be a sufficiently large integer and X be a Dirichlet character modulo q. In this paper, we extend the product x（-1）=-1 L（1, X） with prime q, arising from the Kummer conjecture, to the products of some genera...Let q be a sufficiently large integer and X be a Dirichlet character modulo q. In this paper, we extend the product x（-1）=-1 L（1, X） with prime q, arising from the Kummer conjecture, to the products of some general Dirichlet series, and give some meaningful estimates for them.展开更多
Let p be an odd prime, c be an integer with （c,p） = 1, and let N be a positive integer withN ≤ p - 1. Denote by r（N, c;p） the number of integers a satisfying 1 ≤ a ≤ N and 2 a ＋ a, where a is an integer with...Let p be an odd prime, c be an integer with （c,p） = 1, and let N be a positive integer withN ≤ p - 1. Denote by r（N, c;p） the number of integers a satisfying 1 ≤ a ≤ N and 2 a ＋ a, where a is an integer with 1 ≤a≤ p - 1, aa ≡ c （mod p）. It is well known that r（N, c;p） = 1/2N ＋ O（p1/2log2p）.The main purpose of this paper is to give an asymptotic formula for ∑p-1 c=1（τ（N,c;p）-1/2N）2.展开更多
In this paper we prove that, with at most O（N^5/12＋ε） exceptions, all positive odd integers n ≤ N with n ≡ 0 or 1（mod 3） can be written as a sum of a prime and two squares of primes.
Let q be a power of a prime, F_q a finite field with q elements, b a fixed primitive root of F_q and e a given divisor of q-1. Then the cyclotomic number (h, k )_e of order e in F_q is defined as the number of ordered...Let q be a power of a prime, F_q a finite field with q elements, b a fixed primitive root of F_q and e a given divisor of q-1. Then the cyclotomic number (h, k )_e of order e in F_q is defined as the number of ordered pairs (s, t )展开更多
基金Supported by NSFC(Grant No.11371291)GICF of Northwest University(Grant No.YZZ15009)
文摘The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 2-dimensional Kloostermann sums mod p, and give an exact computational formula for it.
文摘The main purpose of this paper is using the analytic methods, the solutions of the congruence equation mod p and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 3-dimensional Kloostermann sums mod p, and give a sharp asymptotic formula for it.
基金Supported by the Natural Science Basic Research Plan in Shaanxi Province of China(No.2018JM1035)the Young Talent fund of University Association for Science and Technology in Shaanxi,China(No.20170607)。
文摘The main purpose of this paper is, using the analytic method, to study the mean value properties of the complete trigonometric sums with Dirichlet characters, and give an exact calculating formula for its fourth power mean.
文摘In 1923, Hardy and Littlewood[1] conjectured that each integer n can be written asp+m12+ m22 = n,and Linnik[2,3] proved that this conjecture is true. But if these mi with i = 1,2 are restricted to primes Pi, the corresponding result is out of reach at present. We consider the following Diophantine equation
基金Supported by National Natural Science Foundation of China(Grant No.10601039)
文摘Let q be a sufficiently large integer and X be a Dirichlet character modulo q. In this paper, we extend the product x（-1）=-1 L（1, X） with prime q, arising from the Kummer conjecture, to the products of some general Dirichlet series, and give some meaningful estimates for them.
基金Supported by National Natural Science Foundation of China （Grant No. 10601039）
文摘Let p be an odd prime, c be an integer with （c,p） = 1, and let N be a positive integer withN ≤ p - 1. Denote by r（N, c;p） the number of integers a satisfying 1 ≤ a ≤ N and 2 a ＋ a, where a is an integer with 1 ≤a≤ p - 1, aa ≡ c （mod p）. It is well known that r（N, c;p） = 1/2N ＋ O（p1/2log2p）.The main purpose of this paper is to give an asymptotic formula for ∑p-1 c=1（τ（N,c;p）-1/2N）2.
基金Project supported by National Natural Science Foundation(No. 90304009)Foundation of Qufu Normal University for Ph.D.
文摘In this paper we prove that, with at most O（N^5/12＋ε） exceptions, all positive odd integers n ≤ N with n ≡ 0 or 1（mod 3） can be written as a sum of a prime and two squares of primes.
文摘Let q be a power of a prime, F_q a finite field with q elements, b a fixed primitive root of F_q and e a given divisor of q-1. Then the cyclotomic number (h, k )_e of order e in F_q is defined as the number of ordered pairs (s, t )
基金supported by NSFC(No.11571277)the Science and Technology Program of Shaanxi Province of China(No.2014JM1007,No.2014KJXX-61,No.2016GY-080,No.2016GY-077)
