数学与计算机科学 |
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短区间中整数及其逆的分布 |
赵艳1, 吕星星2 |
1.西安文理学院 信息工程学院,陕西 西安 710068 2.西北大学 数学学院,陕西 西安 710127 |
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Distribution of an integer and its inverse in a short interval |
ZHAO Yan1, LYU Xingxing2 |
1.School of Information Engineering, Xi'an University, Xi'an 710068, China 2.School of Mathematics, Northwest University, Xi'an 710127, China);. |
1 APOSTOL T M. Introduction to Analytic Number Theory[M]. New York: Springer-Verlag, 1976. 2 VAN HAMME L. Some conjectures concerning partial sums of generalized hyper geometric series in p-adic functional analysis[J]. Lecture Notes in Pure and Applied Mathematics, 1997, 192: 223-236. 3 PAN H, SUN Z W. A combinatorial identity with application to Catalan numbers[J]. Discrete Math ematics, 2006, 306(16): 1921-1940. DOI: 10.1016/j.disc.2006.03.050 4 ZHAO L L, PAN H, SUN Z W. Congruences for the second-order Catalan numbers[J]. Proceedings of the American Mathematical Society, 2010, 138(1): 37-46. DOI: 10.1090/S0002-9939-09-10067-9 5 DUAN, R, SHEN S M. Bernoulli polynomials and their some new congruence properties[J]. Symmetry, 2019, 11(3): 365. DOI: 10.3390/sym11030365 6 HOU Y W, SHEN S M. The Euler numbers and recursive properties of Dirichlet L-functions[J]. Advances in Difference Equations, 2018: 397. DOI: 10.1186/s13662-018-1853-y 7 ZHANG W P. Some identities involving the Euler and the central factorial numbers[J]. The Fibonacci Quarterly, 1998, 36(2): 154-157. 8 ZHAO J H, CHEN Z Y. Some symmetric identities involving Fubini polynomials and Euler numbers[J]. Symmetry, 2018, 10(8): 303. DOI: 10.3390/sym10080303 9 ZHANG W P, XU Z F. On a conjecture of the Euler numbers[J]. Journal of Number Theory, 2007, 127 (2): 283-291. DOI: 10.1016/j.jnt.2007.04.004 10 CHO B, PARK H. Evaluating binomial convolution sums of divisor functions in terms of Euler and Bernoulli polynomials[J]. International Journal of Number Theory, 2018, 14(2): 509-525. DOI: 10.1142/S1793042118500318 11 WANG L Q, CAI, T X. A curious congruence modulo prime powers[J]. Journal of Number Theory, 2014, 144(14): 15-24. DOI: 10.1016/j.jnt.2014.04.004 12 SUN Z H. Congruences concerning Bernoulli numbers and Bernoulli polynomials[J]. Discrete Applied Mathematics, 2000, 105(1): 193-223. DOI: 10.1016/s0166-218x(00)00184-0 13 ZHOU X, CAI T X. A generalization of a curious congruence on harmonic sums[J]. Proceedings of the American Mathematical Society, 2007, 135(5): 1329-1334. DOI: 10.1090/s0002-9939-06-08777-6 14 CHOWLA S. On Kloosterman's sum[J]. Norkse Vid Selbsk Fak Frondheim, 1967, 40(4): 70-72. 15 IWANIEC H. Topics in Classical Automorphic Forms[M]. Providence: American Mathematical Society Publications, 1997: 61-63. DOI: http://dx.doi.org/10.1090/gsm/017 |
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