In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a se...In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.展开更多
The authors establish an explicit formula for the generalized Euler NumbersE2n^（x）, and obtain some identities and congruences involving the higher＇order Euler numbers, Stirling numbers, the central factorial numbe...The authors establish an explicit formula for the generalized Euler NumbersE2n^（x）, and obtain some identities and congruences involving the higher＇order Euler numbers, Stirling numbers, the central factorial numbers and the values of the Riemann zeta-function.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, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet Lfunction at positive integers...In this paper, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet Lfunction at positive integers by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered.展开更多
文摘In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.
基金the Guangdong Provincial Natural Science Foundation (No.05005928)the National Natural Science Foundation (No.10671155) of P.R.China
文摘The authors establish an explicit formula for the generalized Euler NumbersE2n^（x）, and obtain some identities and congruences involving the higher＇order Euler numbers, Stirling numbers, the central factorial numbers and the values of the Riemann zeta-function.
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Supported by the National Natural Science Foundation of China(Grant No.11326050)
文摘In this paper, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet Lfunction at positive integers by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered.
