Identities and congruences for the general partition and Ramanujan’s tau functions

A. O. L. Atkin, Ramanujan congruences for p −k (n), Canad. J. Math., 20 (1968), 67–78.

N. D. Baraah and K. K. Ojah, Some congruences deducible from Ramanujan’s cubic continued fraction, Int. J. Number Theory, 7 (2011), 1331–1343.

B. C. Berndt, Ramanujan’s Notebooks, Part III, Springer-Verlag, New York, 1991.

B. C. Berndt, Ramanujan’s Notebooks, Part IV, Springer-Verlag, New York, 1994.

B. C. Berndt, C. Gugg and S. Kim, Ramanujan elementary method in partition congruences, in Partitions, q-Series, and Modular Forms, K. alladi and F. Garvan, eds., Springer, New York pp. 13–22, 2011.

B.C. Berndt and K. Ono, Ramanujan’s unpublished manuscript on the partition and tau functions with proofs and commentary, Sém. Lotharingien de Combinatoire 42 (1999), 63 pp.; in The Andrews Festschrift, D. Foata and G.-N. Han, eds., Springer-Verlag, Berlin, 2001, pp. 39–110.

B.C. Berndt, A. J. Yee and J. Yi, Theorems on partition from a page in Ramanujan’s lost notebook, J. Comput. Appl. Math., 160 (2003), 53–68.

M. Boylan, Exceptional congruences for powers of the partition function, Acta Aritk, 111 (2004), 187–203.

H. M. Farkas and I. Kra, Ramanujan partition identities, Contemporary Math., 240 (1999), 111–130.

H. M. Farkas and I. Kra, A function theoretic approach to the Ramanujan partition identities with applications to combinatorial number theory, Contemporary Math., 240 (1999), 131–157.

H. M. Farkas and I. Kra, Three term theta identities, Contemporary Math., 256 (2000), 95–101.

H. M. Farkas and I. Kra, Theta constants, Riemann Surfaces and the Modular Group, Grad. Stud. Math., vol. 37, Amer. Math. Soc, Providence, RI, 2001.

J. M. Gandhi, Congruences for p r(n) and Ramanujan’s τ function, Amer. Math. Monthly, 70 (1963), 265–274.

B. Gordon, Ramanujan congruences for p −k (mod11r), Glasgow Math. J., 24 (1983), 107–123.

M. D. Hirschhorn, An identity of Ramanujan, and applications in q-series from a contemporary perspective, Contemp. Math., 254 (2000), 229–234.

I. Kiming and J. Olsson, Congruences like Ramanujan’s for powers of the partition function, Arch. Math., 59 (1992), 348–360.

J. L. Mordell, On Mr. Ramanujan’s empirical expansions of modular functions, Proc. Cambridge Phillos. Soc, 19 (1917), 117–124.

M. Newman, An identity for the coefficients of certain modular forms, J. Lond. Math. Soc, 30 (1955), 488–493.

M. Newman, Some theorems about pr(n), Canad. J. Math., 9 (1957), 68–70.

M. Newman, Congruences for the coefficients of modular forms and some new congruences for the partition function, Canad. J. Math., 9 (1957), 549–552.

K. G. Ramanathan, Identites and congruences of the Ramanujan type, Canad. J. Math., 2 (1950), 168–178.

S. Ramanujan, On certain arithmetical functions, Trans. Cambridge Phillos. Soc, 22 (1916), 159–184.

S. Ramanujan, Some properties of p(n), the number of partitions of partitions, Proc. Cambridge Phillos. Soc, 19 (1919), 207–210.

S. Ramanujan, Congruence properties of partitions, Proc. Lond. Math. Soc, 18 (1920), xix.

S. Ramanujan, Congruence properties of partitions, Math. Z., 9 (1921), 147–153.

S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988.

G. N. Watson, Theorems stated by Ramanujan (VII): Theorems on continued fractions, J. Lond. Math. Soc, 4 (1929), 39–48.