New Ramanujan type congruences modulo 5 for overpartitions

Andrews, G.E., Berndt, B.C.: Ramanujan’s Lost Notebook, Part I. Springer, New York (2000)

Baruah, N.D., Bora, J., Ojah, K.K.: Ramanujan’s modular equations of degree $$5$$ 5 . Proc. Indian Acad. Sci. 122, 485–506 (2012)

Berndt, B.C.: Ramanujan’s Notebooks, Part III. Springer, New York (1991)

Berndt, B.C.: Number Theory in the Spirit of Ramanujan. American Mathematical Society, Providence (2006)

Berndt, B.C.: Ramanujan’s congruences for the partition function modulo $$5$$ 5 , $$7$$ 7 , and $$11$$ 11 . Int. J. Number Theory 3, 349–354 (2007)

Chen, W.Y.C., Xia, E.X.W.: Proof of a conjecture of Hirschhorn and Sellers on overpartition. Acta Arith. 163, 59–69 (2014)

Chen, W.Y.C., Hou, Q.-H., Sun, L.H., Zhang, L.: Ramanujan-type congruences for overpartitions modulo $$16$$ 16 . Ramanujan J. (2015). doi: 10.1007/s11139-015-9689-5

Chen, W.Y.C., Sun, L.H., Wang, R.H., Zhang, L.: Ramanujan-type congruences for overpartitions modulo 5. J. Number Theory 148, 62–72 (2015)

Hirschhorn, M.D.: An Identity of Ramanujan, and Applications, in $$q$$ q -series from a contemporary Perspective, Contemporary Mathematics, vol. 254. American Mathematical Society, Providence (2000)

Hirschhorn, M.D., Sellers, J.A.: An infinite family of overpartition congruences modulo $$12$$ 12 . Integers 5(1), Article A20 (2005)

Hirschhorn, M.D., Sellers, J.A.: Arithmetic relations for overpartitions. J. Comb. Math. Comb. Comput. 53, 65–73 (2005)

Kim, B.: The overpartition function modulo $$128$$ 128 . Integers 8, Article A38 (2008)

Kim, B.: A short note on the overpartition function. Discret. Math. 309, 2528–2532 (2009)

Lin, B.L.S.: A new proof of a conjecture of Hirschhorn and Sellers on overpartitions. Ramanujan J. 38, 199–209 (2015)

Lovejoy, J., Osburn, R.: Quadratic forms and four partition functions modulo $$3$$ 3 . Integers 11(1), Article A4 (2011)

Mahlburg, K.: The overpartition function modulo small powers of $$2$$ 2 . Discret. Math. 286, 263–267 (2004)

Treneer, S.: Congruences for the coefficients of weakly holomorphic modular forms. Proc. Lond. Math. Soc. 93, 304–324 (2006)

Wang, L.: Another proof of a conjecture of Hirschhorn and Sellers on overpartitions. J. Integer Seq. 17(9), Article 14.9.8 (2014)

Xia, E.X.W.: Congruences modulo $$9$$ 9 and $$27$$ 27 for overpartitions. Ramanujan J.:1–23 (2015). doi: 10.1007/s11139-015-9739-z

Xiong, X.-H.: Overpartition function modulo $$16$$ 16 and some binary quadratic forms. Int. J. Number Theory:1–14 (2015). doi: 10.1142/S1793042116500731

Yao, O.X.M., Xia, E.X.W.: New Ramanujan-like congruences modulo powers of $$2$$ 2 and $$3$$ 3 for overpartitions. J. Number Theory 133, 1932–1949 (2013)