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Abstract ：
The aim of this paper is to correct and improve some results obtained in the paper "Quantitative logic" (C) 2014 Elsevier Inc. All rights reserved.
Keyword ：
Degree of similarity Pseudo-metric Quantitative logic
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| GB/T 7714 | Li, Cheng , Liu, Hua-Wen , Wang, Guo-Jun . Correction and improvement on several results in quantitative logic [J]. | INFORMATION SCIENCES , 2014 , 278 : 555-558 . |
| MLA | Li, Cheng 等. "Correction and improvement on several results in quantitative logic" . | INFORMATION SCIENCES 278 (2014) : 555-558 . |
| APA | Li, Cheng , Liu, Hua-Wen , Wang, Guo-Jun . Correction and improvement on several results in quantitative logic . | INFORMATION SCIENCES , 2014 , 278 , 555-558 . |
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| GB/T 7714 | Ji, Yuanyuan , Wang, Zhidong , Li, Zongfang . Smoking Cessation, Weight Change, and Risk of Cardiovascular Disease [J]. | JAMA-JOURNAL OF THE AMERICAN MEDICAL ASSOCIATION , 2013 , 310 (3) : 322-322 . |
| MLA | Ji, Yuanyuan 等. "Smoking Cessation, Weight Change, and Risk of Cardiovascular Disease" . | JAMA-JOURNAL OF THE AMERICAN MEDICAL ASSOCIATION 310 . 3 (2013) : 322-322 . |
| APA | Ji, Yuanyuan , Wang, Zhidong , Li, Zongfang . Smoking Cessation, Weight Change, and Risk of Cardiovascular Disease . | JAMA-JOURNAL OF THE AMERICAN MEDICAL ASSOCIATION , 2013 , 310 (3) , 322-322 . |
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Abstract ：
Let q be a sufficiently large integer and chi be a Dirichlet character modulo q. In this paper, we extend the product I (chi(-1)=-1) L(1, chi) with prime q, arising from the Kummer conjecture, to the products of some general Dirichlet series, and give some meaningful estimates for them.
Keyword ：
Dirichlet character Dirichlet L-function Kummer conjecture
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| GB/T 7714 | Zhang, Jun Huai , Yi, Yuan , Xi, Ping . On the products arising from the Kummer conjecture [J]. | ACTA MATHEMATICA SINICA-ENGLISH SERIES , 2012 , 28 (8) : 1677-1688 . |
| MLA | Zhang, Jun Huai 等. "On the products arising from the Kummer conjecture" . | ACTA MATHEMATICA SINICA-ENGLISH SERIES 28 . 8 (2012) : 1677-1688 . |
| APA | Zhang, Jun Huai , Yi, Yuan , Xi, Ping . On the products arising from the Kummer conjecture . | ACTA MATHEMATICA SINICA-ENGLISH SERIES , 2012 , 28 (8) , 1677-1688 . |
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Abstract ：
研究了特征和及其算术性质,并利用解析方法得到了两个关于特征和的混合均值的渐近公式,从而推广了特征和的算术性质.
Keyword ：
广义二次高斯和 混合均值 特征和
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| GB/T 7714 | 刘伟霞 , 易媛 . 关于特征和的混合均值 [J]. | 纯粹数学与应用数学 , 2010 , (3) : 490-494,507 . |
| MLA | 刘伟霞 等. "关于特征和的混合均值" . | 纯粹数学与应用数学 3 (2010) : 490-494,507 . |
| APA | 刘伟霞 , 易媛 . 关于特征和的混合均值 . | 纯粹数学与应用数学 , 2010 , (3) , 490-494,507 . |
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Abstract ：
In this paper, we prove an interesting reciprocity formula for a certain case of a general Dedekind sums using analytic methods and the Fourier expansion of the Bernoulli polynomials.
Keyword ：
Bernoulli polynomial Fourier expansion General Dedekind sums reciprocity formula
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| GB/T 7714 | Yi, Yuan . On the general Dedekind sums and its reciprocity formula [J]. | PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES , 2010 , 120 (1) : 1-6 . |
| MLA | Yi, Yuan . "On the general Dedekind sums and its reciprocity formula" . | PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES 120 . 1 (2010) : 1-6 . |
| APA | Yi, Yuan . On the general Dedekind sums and its reciprocity formula . | PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES , 2010 , 120 (1) , 1-6 . |
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Keyword ：
Diophantine equation linear recurrence sequence
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| GB/T 7714 | Hai, Yang , Walsh, P. G. . On a Diophantine problem of Bennett [J]. | ACTA ARITHMETICA , 2010 , 145 (2) : 129-136 . |
| MLA | Hai, Yang 等. "On a Diophantine problem of Bennett" . | ACTA ARITHMETICA 145 . 2 (2010) : 129-136 . |
| APA | Hai, Yang , Walsh, P. G. . On a Diophantine problem of Bennett . | ACTA ARITHMETICA , 2010 , 145 (2) , 129-136 . |
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Abstract ：
Let p be an odd prime and a be an integer coprime with p. Denote by N (a, p) the number of pairs of integers b, c with bc equivalent to a(mod p), 1 <= b, c < p and with b, c having different parity. The main purpose of this paper is to study the mean square value problem of (N (a, p) - 1/2(p - 1)) over interval (N, N + M] with M, N positive integers by using the analytic methods, and finally by obtaining a sharp asymptotic formula.
Keyword ：
Gauss sum Kloosterman sum Lehmer problem
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| GB/T 7714 | Ren, Dongmei , Lu, Yaming . Mean value estimates of the error terms of Lehmer problem [J]. | PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES , 2010 , 120 (4) : 507-513 . |
| MLA | Ren, Dongmei 等. "Mean value estimates of the error terms of Lehmer problem" . | PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES 120 . 4 (2010) : 507-513 . |
| APA | Ren, Dongmei , Lu, Yaming . Mean value estimates of the error terms of Lehmer problem . | PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES , 2010 , 120 (4) , 507-513 . |
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Abstract ：
The main purpose of this paper is to use the M. Toyoizumi's important work, the properties of the Dedekind sums and the estimates for character sums to study a hybrid mean value of the Dedekind sums, and give a sharper asymptotic formula for it.
Keyword ：
Dedekind sums Dirichlet L-function mean value
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| GB/T 7714 | Yang, Hai . A hybrid mean value of the Dedekind sums [J]. | CZECHOSLOVAK MATHEMATICAL JOURNAL , 2010 , 60 (4) : 1055-1063 . |
| MLA | Yang, Hai . "A hybrid mean value of the Dedekind sums" . | CZECHOSLOVAK MATHEMATICAL JOURNAL 60 . 4 (2010) : 1055-1063 . |
| APA | Yang, Hai . A hybrid mean value of the Dedekind sums . | CZECHOSLOVAK MATHEMATICAL JOURNAL , 2010 , 60 (4) , 1055-1063 . |
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Abstract ：
Let n >= 2 be a fixed integer, let q and c be two integers with q > n and (n, q) = (c, q) = 1. For every positive integer a which is coprime with q we denote by (a) over bar (c) the unique integer satisfying 1 <= (a) over bar (c) <= q and a (a) over bar (c) = c(mod q). Put L(q) = {a is an element of Z(+) : (a, q) = 1, n |a + (a) over bar (c)}. The elements of L(q) are called D. H. Lehmer numbers. The main purpose of this paper is to prove that (under natural conditions) every sufficiently large integer can be expressed as the sum of three D. H. Lehmer numbers.
Keyword ：
Circle method DH Lehmer numbers Exponential sums Gauss sums
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| GB/T 7714 | Lu, Yaming , Yi, Yuan . Partitions involving DH Lehmer numbers [J]. | MONATSHEFTE FUR MATHEMATIK , 2010 , 159 (1-2) : 45-58 . |
| MLA | Lu, Yaming 等. "Partitions involving DH Lehmer numbers" . | MONATSHEFTE FUR MATHEMATIK 159 . 1-2 (2010) : 45-58 . |
| APA | Lu, Yaming , Yi, Yuan . Partitions involving DH Lehmer numbers . | MONATSHEFTE FUR MATHEMATIK , 2010 , 159 (1-2) , 45-58 . |
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Abstract ：
In this paper, the general Cochrane sum is defined. The main purpose is to study the mean square value problem of general Cochrane sum by using the estimates for trigonometric sums and the properties of general Kloosterman sum, and finally give a sharp asymptotic formula.
Keyword ：
Cochrane sum Gauss sum Kloosterman sum Legendre's symbol
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| GB/T 7714 | Ren, Dongmei , Yi, Yuan . On the mean value of general Cochrane sum [J]. | PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES , 2010 , 86 (1) : 1A-5A . |
| MLA | Ren, Dongmei 等. "On the mean value of general Cochrane sum" . | PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 86 . 1 (2010) : 1A-5A . |
| APA | Ren, Dongmei , Yi, Yuan . On the mean value of general Cochrane sum . | PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES , 2010 , 86 (1) , 1A-5A . |
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