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        關(guān)于1 1/2 … 1/n的一類初等對稱函數(shù)的2-adic賦值

        2023-04-29 00:44:03邱敏林宗兵譚千蓉
        關(guān)鍵詞:賦值函數(shù)

        邱敏 林宗兵 譚千蓉

        References:

        [1] Theisinger L. Bemerkung über die harmonische Reihe [J]. Monatsh Math Phys, 1915, 26: 132.

        [2] Nagell T. Eine eigenschaft gewisser summen [J]. Skr Norske Vid Akad Kristiania, 1923, 13: 10.

        [3] Erds P, Niven I. Some properties of partial sums of the harmonic series [J]. Bull Amer Math Soc, 1946, 52: 248.

        [4] Chen Y G, Tang M. On the elementary symmetric functions of 1, 1/2, …, 1/n [J]. Amer Math Monthly, 2012, 119: 862.

        [5] Hong S F, Wang C L. The elementary symmetric functions of reciprocal arithmetic progressions [J]. Acta Math Hungari, 2014, 144: 196.

        [6] Feng Y L, Hong S F, Jiang X, et al. A generalization of a theorem of Nagell [J]. Acta Math Hungar, 2019, 157: 522.

        [7] Wang C L, Hong S F. On the integrality of the elementary symmetric functions of 1, 1/3, …,1/(2n-1) [J]. Math Slovaca, 2015, 65: 957.

        [8] Luo Y Y, Hong S F, Qian G Y, et al.The elementary symmetric functions of a reciprocal polynomial sequence [J]. C R Math Acad Sci Paris, 2014, 352: 269.

        [9] Feng Y L, Zhao W. On the integrality of the second elementary symmetric function of 1,1/3s1,…,1/(2n-1)sn-1 [J]. J Sichuan Univ: Nat Sci Ed, 2020, 57: 431.

        [10] Wolstenholm J. On certain properties of prime numbers [J]. Quart J Pure Appl Math, 1862, 5: 35.

        [11] Eswarathasan A, Levine E. p-integral harmonic numbers [J]. Discrete Math, 1991, 91: 249.

        [12] Boyd D. A p-adic study of the partial sums of the harmonic series [J]. Experiment Math, 1994, 3: 287.

        [13] Kamano K. On 3-adic valuations of generalized harmonic numbers [J]. Integers, 2012, 12: 311.

        [14] Sanna C. On the p-adic valuation of harmonic numbers [J]. J Number Theory, 2016, 166: 41.

        [15] Sun Q, Hong S F. A p-adic proof of Wolstenholm's Theorem and its generalizations [J]. J Sichuan Univ: Nat Sci Ed, 1999, 36: 840.

        [16] Wu B L, Chen Y G. On certain properties of harmonic numbers [J]. J Number Theory, 2017, 175: 66.

        [17] Leonetti P, Sanna C. On the p-adic valuation of Stirling numbers of the first kind [J]. Acta Math Hungari, 2017, 151: 217.

        [18] Lengyel T. On p-adic properties of the Stirling numbers of the first kind [J]. J Number Theory, 2015, 148: 73.

        [19] Komatsu T, Young P. Exact p-adic valuations of Stirling numbers of the first kind [J]. J Number Theory, 2017, 177: 20.

        [20] Qiu M, Hong S F. 2-adic valuations of Stirling numbers of the first kind [J]. Int J Number Theory, 2019, 15: 1827.

        [21] Hong S F, Qiu M. On the p-adic properties of Stirling numbers of the first kind [J]. Acta Math Hungari, 2020, 161: 366.

        [22] Qiu M, Feng Y L, Hong S F. 3-Adic valuations of Stirling numbers of the first kind [EB/OL]. [2022-11-30]. https://arxiv.org/abs/2109.13458.

        [23] Feng Y L, Qiu M. Some results on p-adic valuations of Stirling numbers of the second kind [J]. AIMS Math, 2020, 5: 4168.

        [24] Hong S F. On the p-adic behaviors of Stirling numbers of the first and second kinds [J]. RIMS Kokyuroku Bessatsu, 2020, 2162: 104.

        [25] Hong S F, Zhao J R, Zhao W. The 2-adic valuations of Stirling numbers of the second kind [J]. Int J Number Theory, 2012, 8: 1057.

        [26] Hong S F, Zhao J R, Zhao W. The universal Kummer congruences [J]. J Aust Math Soc, 2013, 94: 106.

        [27] Zhao J R, Hong S F, Zhao W. Divisibility by 2 of Stirling numbers of the second kind and their differences [J]. J Number Theory, 2014, 140: 324.

        [28] Zhao W, Qiu M. Some new results on the p-adic valuations of Stirling numbers of the second kind [J]. J Sichuan Univ: Nat Sci Ed, 2020, 57: 865.

        [29] Zhao W, Zhao J R, Hong S F. The 2-adic valuations of differences of Stirling numbers of the second kind [J]. J Number Theory, 2015, 153: 309.

        [30] Koblitz N. p-adic numbers, p-adic analysis and zeta-functions [M]. New York: Springer-Verlag, 1984.

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