数学与计算机科学 |
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关于伯努利多项式和Dirichlet L-函数的均值问题 |
张艺雪 |
西北大学 数学学院, 陕西 西安 710127 |
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On the Bernoulli polynomials and mean square value of the Dirichlet L-functions |
ZHANG Yixue |
School of Mathematics, Northwest University, Xi’an 710127, China |
1 WALUM H . An exact formula for an average of L-Series[J]. Illinois Journal of Mathematics, 1982, 26(1): 1-3. DOI:10.1215/ijm/1256046895 2 ZHANG W P . On the mean values of Dedekind sums[J]. Journal de Theorie des Nombers, 1996, 8(2): 429-442. DOI:10.5802/jtnb.179 3 ZHANG W P . Lecture Notes in Contemporary Mathematics[M]. Beijing: Science Press,1989: 173-179. 4 ZHANG W P . Moments of generalized quadratic Gauss sums weighted by L-functions[J]. Journal of Number Theory, 2002,92(2): 304-314. 5 华罗庚 . 数论导论[M]. 北京:科学出版社,1979. HUA L G . Introduction to Number Theory [M]. Beijing: Science Press, 1979. 6 朱敏慧,杨晓柳 .关于L-函数一类二次均值的计算公式[J]. 陕西师范大学学报(自然科学版),2017,45(4):19-22. ZHU M H, YANG X L . On the computational formula of one kind mean square value of L-functions [J]. Journal of Shaanxi Normal University(Natural Science Edition), 2017,45 (4): 18-22. 7 张文鹏 .关于L-函数一类二次均值的注释[J].西北大学学报(自然科学版),1990,20(3):9-12. ZHANG W P . On a note of class mean square values of L-functions[J]. Journal of Northwest University(Natural Science Edition), 1990,20 (3):9-12. 8 BAYAD A, RAOUJ A . Mean values of L-functions and Dedekind sums[J]. Journal of Number Theory, 2012,132(8): 1645-1652. 9 HU S, KIM D, KIM M S . On the integral of the product of four and more Bernoulli polynomials[J]. Ramanujan Journal,2014,33 (2): 281-293.DOI:10.1007/s11139-013-9506-y 10 CARLITZ L . Note on the integral of product of several Bernoulli polynomials [J]. Journal of the London Mathematical Society,1959,34 (3):361-363.DOI:10.1112/jlms/s1-34.3.361 11 ESPINOSA O, MOLL V H . On some integrals involving the Hurwitz Zeta function: Part 2[J].The Ramanujan Journal,2002,6(4): 449-468. 12 APOSTOL T M . Introduction to Analytic Number Theory[M]. New York: Springer-Verlag, 1976. 13 IRELAND K, ROSEN M . A Classical Introduction to Modern Number Theory[M]. New York: Springer-Verlag, 1982. DOI:10.2307/3619180 14 BAYAD A, KIM D . Mean value of products of L-functions and Bernoulli polynomials[J]. Mathematics, 2018, 6(12): 337.DOI:10.3390/math6120337 15 HECKE E . Analytische Arithmetik der Positiven Quadratischen Formen, Mathematische Werke[M]. Copenhagen: Denmark, 1940: 789-918. 16 SHEN S M, CHEN L . Some types of identities involving the Legendre polynomials[J]. Mathematics, 2019, 7(2): 114. DOI:10.3390/math7020114 17 ZHANG W P, CHEN L . On the Catalan numbers and some of their identities[J]. Symmetry,2019, 11(1):62. DOI:10.3390/sym11010062 18 ZHANG Y X, CHEN Z Y . A new identity involving the Chebyshev polynomials[J]. Mathematics,2018, 6(11): 244. DOI:10.3390/math6110244 19 MA Y K, ZHANG W P . Some identities involving Fibonacci polynomials and Fibonacci numbers[J]. Mathematics, 2018, 6(12): 334.DOI:10.3390/math6120334 20 CHEN G H, CHEN L . Some identities involving the Fubini polynomials and Euler polynomials[J]. Mathematics,2018, 6(12): 300.DOI:10.3390/math6120300 21 KIM T . Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on Z P [J]. Russian Journal Of Mathematical Physics, 2009,16(1): 93-96. 22 KIM T, KIM D S, JANG G W, et al . Symmetric identities for Fubini polynomials[J]. Symmetry,2018,10 (6): 219. DOI:10.3390/sym10060219 23 KIM D S, PARK K H . Identities of symmetry for Bernoulli polynomials arising from quotients of Volkenborn integrals invariant under S 3 [J]. Applied Mathematics and Computation, 2013,219(10): 5096-5104. DOI:10.1016/j.amc.2012.11.061 24 ZHAO J H, CHEN Z Y . Some symmetric identities involving Fubini polynomials and Euler numbers[J]. Symmetry, 2018,10(8): 303. |
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