Related papers: Universal mock theta functions and two-variable He…
Bringmann, Lovejoy, and Osburn showed that the generating functions of the spt-overpartition functions spt(n), spt1(n), spt2(n), and M2spt(n) are quasimock theta functions, and satisfy a number of simple Ramanujan-like congruences. Andrews,…
In this paper, we develop a unified method for obtaining and proving $m$-dissections of mock theta functions. Our approach builds upon a transformation formula for Appell--Lerch sums due to Hickerson and Mortenson, which allows these sums…
It was recently shown that $q\omega(q)$, where $\omega(q)$ is one of the third order mock theta functions, is the generating function of $p_{\omega}(n)$, the number of partitions of a positive integer $n$ such that all odd parts are less…
We prove that the generating function of overpartition $M2$-rank differences is, up to coefficient signs, a component of the vector-valued mock Eisenstein series attached to a certain quadratic form. We use this to compute analogs of the…
In this paper, we establish simple $k$-fold summation expressions for the Quot and motivic Cohen--Lenstra zeta functions associated with the $(2,2k)$ torus links. Such expressions lead us to some multiple Rogers--Ramanujan type identities…
We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric…
We exhibit an infinite family of vector-valued mock theta functions indexed by positive integers coprime to $6$. These are built from specializations of Dyson's rank generating function and related functions studied by Watson, Gordon, and…
The Kronecker theta function is a quotient of the Jacobi theta functions, which is also a special case of Ramanujan's $_1\psi_1$ summation. Using the Kronecker theta function as building blocks, we prove a decomposition theorem for theta…
We compute the Moore-Witten regularized u-plane integral on CP^2, and we confirm their conjecture that it is the generating function for the SO(3)-Donaldson invariants of CP^2. We prove this conjecture using the theory of mock theta…
We show that some $q$-series such as universal mock theta functions are linear sums of theta quotients and mock Jacobi forms of weight 1/2, which become holomorphic parts of real analytic modular forms when they are restricted to torsion…
We demonstrate how formulas that express Hecke-type double-sums in terms of theta functions and Appell--Lerch functions -- the building blocks of Ramanujan's mock theta functions -- can be used to give general string function formulas for…
In his deathbed letter to Hardy, Ramanujan gave a vague definition of a mock modular function: at each root of unity its asymptotics matches the one of a modular form, though a choice of the modular function depends on the root of unity.…
We use a generalized Lambert series identity due to the first author to present q-series proofs of recent results of Imamoglu, Raum and Richter concerning recursive formulas for the coefficients of two 3rd order mock theta functions.…
We define two-parameter generalizations of two combinatorial constructions of Andrews: the kth symmetrized rank moment and the k-marked Durfee symbol. We prove that three specializations of the associated generating functions are so-called…
The generalization of new mock theta functions of Andrews and Bringmann et al are given. Further we have given the expansion of these bilateral generalized new mock theta functions as 2 phi 1 series by Slaters transformation. After that we…
Recently, Bringmann and Kane established two new Bailey pairs and used them to relate certain q-hypergeometric series to real quadratic fields. We show how these pairs give rise to new mock theta functions in the form of q-hypergeometric…
Page 27 of Ramanujan's Lost Notebook contains a beautiful identity which not only gives, as a special case, a famous modular relation between the Rogers-Ramanujan functions $G(q)$ and $H(q)$ but also a relation between two fifth order mock…
In the paper, we give partition-theoretic results for the coefficients of some mock theta functions and prove their congruence properties. Some recurrence relations connecting the coefficients of the mock theta functions with certain…
In recent work where Matsusaka generalizes the relationship between Habiro-type series and false theta functions after Hikami, five families of Hecke-type double-sums of the form \begin{equation*} \left( \sum_{r,s\ge 0…
Partitions associated with mock theta functions have received a great deal of attention in the literature. Recently, Choi and Kim derived several partition identities from the third and sixth order mock theta functions. In addition, three…