Skip to main content Accessibility help


  • BERNARD L. S. LIN (a1)


Recently, Brietzke, Silva and Sellers [‘Congruences related to an eighth order mock theta function of Gordon and McIntosh’, J. Math. Anal. Appl.479 (2019), 62–89] studied the number $v_{0}(n)$ of overpartitions of $n$ into odd parts without gaps between the nonoverlined parts, whose generating function is related to the mock theta function $V_{0}(q)$ of order 8. In this paper we first present a short proof of the 3-dissection for the generating function of $v_{0}(2n)$ . Then we establish three congruences for $v_{0}(n)$ along certain progressions which are subsequences of the integers  $4n+3$ .



Hide All

This work was supported by the National Natural Science Foundation of China (no. 11871246), the Natural Science Foundation of Fujian Province of China (no. 2019J01328) and the Program for New Century Excellent Talents in Fujian Province University (no. B17160).



Hide All
[1]Andrews, G. E., Dixit, A. and Yee, A. J., ‘Partitions associated with the Ramanujan/Watson mock theta functions 𝜔(q), 𝜈(q) and 𝜙(q)’, Res. Number Theory 1 (2015), article 19.
[2]Andrews, G. E., Hirschhorn, M. D. and Sellers, J. A., ‘Arithmetic properties of partitions with even parts distinct’, Ramanujan J. 23 (2010), 169181.
[3]Andrews, G. E., Passary, D., Sellers, J. A. and Yee, A. J., ‘Congruences related to the Ramanujan/Watson mock theta functions 𝜔(q) and 𝜈(q)’, Ramanujan J. 43 (2017), 347357.
[4]Berndt, B. C., Ramanujan’s Notebooks, Part III (Springer, New York, 1991).
[5]Berndt, B. C., Number Theory in the Spirit of Ramanujan (American Mathematical Society, Providence, RI, 2006).
[6]Brenti, F., ‘Determinants of super-Schur functions, lattice paths, and dotted plane partitions’, Adv. Math. 98 (1993), 2764.
[7]Brietzke, E. H. M., Silva, R. and Sellers, J. A., ‘Congruences related to an eighth order mock theta function of Gordon and McIntosh’, J. Math. Anal. Appl. 479 (2019), 6289.
[8]Bringmann, K. and Lovejoy, J., ‘Overpartitions and class numbers of binary quadratic forms’, Proc. Natl. Acad. Sci. USA 106 (2009), 55135516.
[9]Chan, S. H., ‘Congruences for Ramanujan’s 𝜙 function’, Acta Arith. 153 (2012), 161189.
[10]Chan, S. H. and Mao, R., ‘Two congruences for Appell–Lerch sums’, Int. J. Number Theory 8(1) (2012), 111123.
[11]Chen, W. Y. C. and Xia, E. X. W., ‘Proof of a conjecture of Hirschhorn and Sellers on overpartitions’, Acta Arith. 163 (2014), 5969.
[12]Corteel, S. and Lovejoy, J., ‘Overpartitions’, Trans. Amer. Math. Soc. 356 (2004), 16231635.
[13]Dou, D. Q. J. and Lin, B. L. S., ‘New Ramanujan type congruences modulo 5 for overpartitions’, Ramanujan J. 44 (2017), 401410.
[14]Hickerson, D. R. and Mortenson, E. T., ‘Hecke-type double sums, Appell–Lerch sums, and mock theta functions, I’, Proc. Lond. Math. Soc. 109 (2014), 382422.
[15]Hirschhorn, M. D., The Power of q. A Personal Journey (Springer, Cham, 2017).
[16]Hirschhorn, M. D. and Sellers, J. A., ‘Arithmetic relations for overpartitions’, J. Combin. Math. Combin. Comput. 53 (2005), 6573.
[17]Kang, S.-J. and Kwon, J.-H., ‘Crystal bases of the Fock space representations and string functions’, J. Algebra 280 (2004), 313349.
[18]Lebesgue, V. A., ‘Sommation de quelques series’, J. Math. Pures Appl. 5 (1840), 4271.
[19]Lovejoy, J., ‘Overpartitions and real quadratic fields’, J. Number Theory 106 (2004), 178186.
[20]Mao, R., ‘Two identities on the mock theta function V 0(q)’, J. Math. Anal. Appl. 479 (2019), 122134.
[21]McIntosh, R. J., ‘Second order mock theta functions’, Canad. Math. Bull. 50 (2007), 284290.
[22]Wang, L., ‘New congruences for partitions related to mock theta functions’, J. Number Theory 175 (2017), 5165.
MathJax is a JavaScript display engine for mathematics. For more information see


MSC classification


  • BERNARD L. S. LIN (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed