Some properties of $p(n)$ and $c(n)$ modulo powers of $13$
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- by A. O. L. Atkin and J. N. O’Brien
- Trans. Amer. Math. Soc. 126 (1967), 442-459
- DOI: https://doi.org/10.1090/S0002-9947-1967-0214540-7
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References
- J. N. O’Brien, Some properties of partitions with special reference to primes other than 5, 7, and 11, Ph.D. Thesis, Univ. of Durham, England, 1966.
G. N. Watson, Ramanujans Vermutung über Zerfällungsanzahlen, J. Reine Angew. Math. 179 (1938), 97-128.
- Joseph Lehner, Divisibility properties of the Fourier coefficients of the modular invariant $j(\tau )$, Amer. J. Math. 71 (1949), 136–148. MR 27801, DOI 10.2307/2372101
- Joseph Lehner, Further congruence properties of the Fourier coefficients of the modular invariant $j(\tau )$, Amer. J. Math. 71 (1949), 373–386. MR 27802, DOI 10.2307/2372252
- A. O. L. Atkin, Proof of a conjecture of Ramanujan, Glasgow Math. J. 8 (1967), 14–32. MR 205958, DOI 10.1017/S0017089500000045
- Morris Newman, Periodicity modulo $m$ and divisibility properties of the partition function, Trans. Amer. Math. Soc. 97 (1960), 225–236. MR 115981, DOI 10.1090/S0002-9947-1960-0115981-2
- Morris Newman, Congruences for the coefficients of modular forms and for the coefficients of $j(\tau )$, Proc. Amer. Math. Soc. 9 (1958), 609–612. MR 98729, DOI 10.1090/S0002-9939-1958-0098729-6
- Morris Newman, Congruences for the coefficients of modular forms and some new congruences for the partition function, Canadian J. Math. 9 (1957), 549–552. MR 92801, DOI 10.4153/CJM-1957-062-1
- Morris Newman, Further identities and congruences for the coefficients of modular forms, Canadian J. Math. 10 (1958), 577–586. MR 98081, DOI 10.4153/CJM-1958-058-4 S. Ramanujan, On certain arithmetical functions, Trans. Cambridge Philos. Soc. 22 (1916), 159-184. L. J. Mordell, On Mr. Ramanujan’s empirical expansions of modular functions, Proc. Cambridge Philos. Soc. 19 (1919), 117-124.
Bibliographic Information
- © Copyright 1967 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 126 (1967), 442-459
- MSC: Primary 10.21
- DOI: https://doi.org/10.1090/S0002-9947-1967-0214540-7
- MathSciNet review: 0214540