Let p > 5 be a prime. We prove congruences modulo p(3-d) for sums of the general form Sigma((p -3)/2)(k=0) ((2k)(k))t(k)/(2k + 1)(d+1) and Sigma((p-1)/2)(k=1) ((2k)(k))t(k)/kd with d = 0, 1. We also consider the special case t = (-1)(d)/16 of the former sum, where the congruences hold modulo p(5-d).
Pilehrood, K., Pilehrood, T., Tauraso, R. (2012). Congruences concerning Jacobi polynomials and Apery-like formulae. INTERNATIONAL JOURNAL OF NUMBER THEORY, 8(7), 1789-1811 [10.1142/S1793042112501035].
Congruences concerning Jacobi polynomials and Apery-like formulae
TAURASO, ROBERTO
2012-01-01
Abstract
Let p > 5 be a prime. We prove congruences modulo p(3-d) for sums of the general form Sigma((p -3)/2)(k=0) ((2k)(k))t(k)/(2k + 1)(d+1) and Sigma((p-1)/2)(k=1) ((2k)(k))t(k)/kd with d = 0, 1. We also consider the special case t = (-1)(d)/16 of the former sum, where the congruences hold modulo p(5-d).File in questo prodotto:
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[2012] Congruences concerning Jacobi polynomials and Apery-like formulae.pdf
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