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Ramanujan Congruences For p-k(n) Modulo Powers Of 17

Published online by Cambridge University Press:  20 November 2018

Kim Hughes
Kim Hughes*
Affiliation:
Department of Mathematics California State University San Bernardino, California
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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.

Keywords

11F3311P7611F2011F3011F0805A17
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 3 , 01 June 1991 , pp. 506 - 525
Copyright
Copyright © Canadian Mathematical Society 1991

References

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. Atkin, A.O.L. , Congruences for modular forms. Computers in mathematical research (North-Holland, Amsterdam, 1968), 8–19.Google Scholar
3. L, A.O.. Atkin, Ramanujan congruences for p-k (n), Can. J. Math. 20(1968), 67–78.Google Scholar
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. Gordon, B., Ramanujan congruences for p-k, (mod 1 lr), Glasgow Math. J., 24(1983), 107–123.Google Scholar
6. Hughes, K., Arithmetic properties of modular forms. Ph.D. Thesis, University of California, Los Angeles, 1980.Google Scholar
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. Newman, M., Remarks on some modular identities, Trans. Amer. Math. Soc, 73(1952), 313–320.Google Scholar