陳國(guó)華

(華北水利水電大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院,河南鄭州 450011)

關(guān)于連續(xù)素?cái)?shù)上取值的Legend re符號(hào)和的估計(jì)

陳國(guó)華

(華北水利水電大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院,河南鄭州 450011)

連續(xù)素?cái)?shù);Legendre符號(hào);非顯然估計(jì)

DO I：10.3969/j.issn.1008-5513.2013.04.012

1 引言及主要結(jié)果

2 引理及其證明

3 定理證明

參考文獻(xiàn)

[1]V inogradov IM.Sur la distribution des residus et des nonresidus des puissances[J].Zh.Fiz.Mat.Obshch. Perm.Gos.Univ.,1918,1:94-98.

[2]V inogradov IM.On the distribution of quad ratic residues and nonresidues[J].Zh.Fiz.M at.Sb.3. 1938,45:311-319.

[3]V inogradov IM.New app roach to the estimation of sum valuesχ(p+k)[J].Izv.Akad.Nauk SSSR Ser. M at.,1952,16:197-210.

[4]Perelmuter G I.Evaluation of a sum containing p rimes[J].Dok l.Akad.Nauk SSSR,1962,144:48-51.

[5]V inogradov IM.Im provement of an estimate for the sum of the valuesχ(p+k)[J].Izv.Akad.Nauk SSSR Ser.Mat.,1953,17:285-290.

[6]Karatsuba A A.Sum s of characters over prim e numbers[J].M ath.USSR Izvestija.,1970,4:303-325.

[7]Karatsuba A A.Sum s of legend re symbols of polynom ials of second degree over prime numbers[J].M ath. USSR Izvestija,1978,12:299-308.

[8]Karatsuba A A.Distribu tion of the values of legend re symbols in polynom ials w ith p rim e numbers[J].Dok l. Akad.Nauk SSSR,1978,238:524-526.

[9]Karatsuba A A.Sum s of characters w ith p rime numbers in an arithmetic p rogression[J].M ath.USSR Izvestija,1971,5:485-501.

[10]Karatsuba A A.The d istribu tion of pairs of quad ratic residues and nonresidues of a special form[J].M ath. USSR.Izvestija,1988,31:307-323.

[11]Karatsuba A A.Non linear character sum s over p rimes[J].Dokl.Math.,2008,2:209-218.

[12]Karatsuba A A.Sum s of characters w ith p rime numbers and their applications[J].Tatra M t.M ath., 2000,20:155-162.

Sum s of Legend re sym bols over consecu tive p rim e num bers

Chen Guohua

(College of M athematics and In formation Science,North China University ofWater Resources And E lectric Power,Zhengzhou 450011,China)

consecutive prim es,legendre sym bols,nontrivial estim ate

O156.4

A

1008-5513(2013)04-0414-11

2008-02-10.

華北水利水電大學(xué)研究生創(chuàng)新課題(YK 2012-08).

陳國(guó)華(1989-),碩士生,研究方向：數(shù)論及其應(yīng)用.

2010 M SC:11A15