Zobrazeno 1 - 10
of 865
pro vyhledávání: '"Ramanujan theta function"'
Publikováno v:
Journal of Algebraic Combinatorics. 55:1031-1062
George Andrews and Ae Ja Yee recently established beautiful results involving bivariate generalizations of the third-order mock theta functions $$\omega (q)$$ and $$\nu (q)$$ , thereby extending their earlier results with the second author. Generaliz
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a481e7746a365f5536f5a2aab59398a9
https://doi.org/10.1007/s10801-021-01082-2
https://doi.org/10.1007/s10801-021-01082-2
Autor:
Chun Wang, Hanfei Song
Publikováno v:
The Ramanujan Journal. 58:1095-1112
In this paper, we obtain some Hecke-type triple sums for the third-order mock theta function $$\omega (q)$$ and the fifth-order mock theta functions $$\chi _0(q)$$ , $$\chi _1(q)$$ . In addition, we extend this topic to the generating function of $$S
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ea9106ce44d65f294270b19422460e33
https://doi.org/10.1007/s11139-021-00499-4
https://doi.org/10.1007/s11139-021-00499-4
Autor:
J. G. Bradley-Thrush
Publikováno v:
The Ramanujan Journal. 57:291-367
A number of equations involving the Appell–Lerch function, $$ \mu $$ , are derived. Emphasis is placed on equations which are analogous to certain linear relations which exist between theta functions, as well as equations which make explicit the sy
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f310172a541f59f8ac8a4d4366540f65
https://doi.org/10.1007/s11139-021-00445-4
https://doi.org/10.1007/s11139-021-00445-4
Autor:
Xiang Zhao, Ernest X. W. Xia
Publikováno v:
The Ramanujan Journal. 58:1259-1284
In 2002, Berkovich and Garvan introduced the $$M_2$$ -rank of partitions without repeated odd parts. Let $$N_2(a, M, n)$$ denote the number of partitions of n without repeated odd parts in which $$M_2$$ -rank is congruent to a mod M. Lovejoy and Osbu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4560cc8e78435139955141108b34c88d
https://doi.org/10.1007/s11139-021-00486-9
https://doi.org/10.1007/s11139-021-00486-9
Autor:
Alice X.H. Zhao
Publikováno v:
International Journal of Number Theory. 18:743-755
We introduce a statistic on overpartitions called the [Formula: see text]-rank. When there are no overlined parts, this coincides with the [Formula: see text]-rank of a partition introduced by Garvan. Moreover, it reduces to the D-rank of an overpart
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e6777156636c1123be36a179ecc7bbc2
https://doi.org/10.1142/s1793042122500397
https://doi.org/10.1142/s1793042122500397
Autor:
Bernard L. S. Lin, Jiejuan Xiao
Publikováno v:
Indian Journal of Pure and Applied Mathematics. 52:141-148
Let $$p_{\omega }(n)$$ be the number of partitions of n in which each odd part is less than twice the smallest part, and assume that $$p_{\omega }(0)=0$$ . Andrews, Dixit, and Yee proved that the generating function of $$p_{\omega }(n)$$ equals $$q\o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9d32a1c2d22520df414a4ed00c193058
https://doi.org/10.1007/s13226-021-00078-9
https://doi.org/10.1007/s13226-021-00078-9
Autor:
Edward Y. S. Liu
Publikováno v:
The Ramanujan Journal. 56:911-929
Andrews introduced odd Durfee symbols to give an interesting combinatorial interpretation of $$\omega (q)$$ invoked by MacMahon’s modular partitions, where $$\omega (q)$$ is one of the mock theta functions defined by Watson. In analogy with Dyson
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::caa53ccbf0fd29f6a9df38a642e686a3
https://doi.org/10.1007/s11139-020-00329-z
https://doi.org/10.1007/s11139-020-00329-z
Autor:
Nancy S. S. Gu, Su-Ping Cui
Publikováno v:
International Journal of Number Theory. 17:1569-1582
An odd Durfee symbol of [Formula: see text] is an array of positive odd integers and a subscript [Formula: see text], [Formula: see text] such that [Formula: see text], [Formula: see text], and [Formula: see text]. Andrews defined the odd rank of an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ce27854be23fca1728e2f7e78e061f00
https://doi.org/10.1142/s1793042121500482
https://doi.org/10.1142/s1793042121500482
Autor:
Shruti Sharma, Meenakshi Rana
Publikováno v:
Electronic Research Archive. 29:1803-1818
The goal of this paper is to provide a new combinatorial meaning to two fifth order and four sixth order mock theta functions. Lattice paths of Agarwal and Bressoud with certain modifications are used as a tool to study these functions.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f706d13ccbe9c75df8644f1e80131726
https://doi.org/10.3934/era.2020092
https://doi.org/10.3934/era.2020092
Autor:
Hannah Burson
Publikováno v:
International Journal of Number Theory. 17:285-295
We introduce combinatorial interpretations of the coefficients of two second-order mock theta functions. Then, we provide a bijection that relates the two combinatorial interpretations for each function. By studying other special cases of the multiva
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8cb9f971b31d38a38c3aabf4a534ae48
https://doi.org/10.1142/s1793042120400229
https://doi.org/10.1142/s1793042120400229