Geodesic
Ramanujan Congruences For p-k (n) Modulo Powers Of 17
Canadian journal of mathematics, Tome 43 (1991) no. 3, pp. 506-525

Voir la notice de l'article provenant de la source Cambridge University Press

For each integer r we define the sequence pr(n) by We note that p-1(n) = p(n), the ordinary partition function. On account of this some authors set r = — k to make positive values of k correspond to positive powers of the generating function for p(n): We follow this convention here. In [3], Atkin proved the following theorem.
DOI : 10.4153/CJM-1991-031-0
Mots-clés : 11F33, 11P76, 11F20, 11F30, 11F08, 05A17 
Hughes, Kim. Ramanujan Congruences For p-k (n) Modulo Powers Of 17. Canadian journal of mathematics, Tome 43 (1991) no. 3, pp. 506-525. doi: 10.4153/CJM-1991-031-0
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[1] 1. L, A.O.. Atkin, Congruence Hecke operators. Number Theory, Proc. Sympos. Pure Math., Vol. XII, Houston, Tex., 1967, Amer. Math. Soc, Providence, R.I., 1969, 33–40. Google Scholar

[2] 2. Atkin, A.O.L. , Congruences for modular forms. Computers in mathematical research (North-Holland, Amsterdam, 1968), 8–19. Google Scholar

[3] 3. L, A.O.. Atkin, Ramanujan congruences for p-k (n), Can. J. Math. 20(1968), 67–78. Google Scholar

[4] 4. L, A.O. Atkin and O, J.N.'Brien, Some properties of p(n) and c(n) modulo powers of 13, Trans. Amer. Math. Soc, 126(1967), 442-159. Google Scholar

[5] 5. Gordon, B., Ramanujan congruences for p-k, (mod 1 lr), Glasgow Math. J., 24(1983), 107–123. Google Scholar

[6] 6. Hughes, K., Arithmetic properties of modular forms. Ph.D. Thesis, University of California, Los Angeles, 1980. Google Scholar

[7] 7. Newman, M., Construction and application of a class of modular functions, II, Proc. London Math. Soc. (3) 9(1959), 373–387. Google Scholar

[8] 8. Newman, M., Remarks on some modular identities, Trans. Amer. Math. Soc, 73(1952), 313–320. Google Scholar

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