Some restricted partition functions: Congruences modulo $7$
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- by D. B. Lahiri PDF
- Trans. Amer. Math. Soc. 140 (1969), 475-484 Request permission
References
- George E. Andrews, An analytic proof of the Rogers-Ramanujan-Gordon identities, Amer. J. Math. 88 (1966), 844–846. MR 202616, DOI 10.2307/2373082 L. E. Dickson, History of the theory of numbers, Vol. I, Chelsea, New York, 1952.
- Basil Gordon, A combinatorial generalization of the Rogers-Ramanujan identities, Amer. J. Math. 83 (1961), 393–399. MR 123484, DOI 10.2307/2372962
- G. H. Hardy, Ramanujan. Twelve lectures on subjects suggested by his life and work, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1940. MR 0004860 G. H. Hardy and E. M. Wright, 4th ed., An introduction to the theory of numbers, Oxford Univ. Press, New York, 1960.
- D. B. Lahiri, On a type of series involving the partition function with applications to certain congruence relations, Bull. Calcutta Math. Soc. 38 (1946), 125–132. MR 19664
- D. B. Lahiri, On Ramanujan’s function $\tau (n)$ and the divisor function $\sigma _k(n)$. I, Bull. Calcutta Math. Soc. 38 (1946), 193–206. MR 20591
- K. G. Ramanathan, Congruence properties of Ramanujan’s function $\tau (n)$. II, J. Indian Math. Soc. (N.S.) 9 (1945), 55–59. MR 16391
- J. M. Rushforth, Congruence properties of the partition function and associated functions, Proc. Cambridge Philos. Soc. 48 (1952), 402–413. MR 49933, DOI 10.1017/S0305004100027808
- G. N. Watson, Über Ramanujansche Kongruenzeigenschaften der Zerfällungsanzahlen. (I), Math. Z. 39 (1935), no. 1, 712–731 (German). MR 1545532, DOI 10.1007/BF01201388
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 140 (1969), 475-484
- MSC: Primary 10.48
- DOI: https://doi.org/10.1090/S0002-9947-1969-0242784-9
- MathSciNet review: 0242784