Related papers: Mock Theta Functions

We give evaluations of certain Borwein's theta functions which appear in Ramanujan theory of alternative elliptic modular bases. Most of this theory where developed by B.C. Berndt, S. Bhargava and F.G. Garvan. We also study the most general…

Recently, Garthwaite-Penniston have shown that the coefficients of Ramanujan's mock theta function $\omega$ satisfy infinitely many congruences of Ramanujan-type. In this work we give the first explicit examples of congruences for…

We evaluate regularized theta lifts for Lorentzian lattices in three different ways. In particular, we obtain formulas for their values at special points involving coefficients of mock theta functions. By comparing the different…

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…

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 describe a family of indefinite theta functions of signature $(1,1)$ that can be expressed in terms of trace functions of vertex algebras built from cones in lattices. The family of indefinite theta functions considered has interesting…

Congruences of Fourier coefficients of modular forms have long been an object of central study. By comparison, the arithmetic of other expansions of modular forms, in particular Taylor expansions around points in the upper-half plane, has…

We give simple proofs of Hecke-Rogers indefinite binary theta series identities for the two Ramanujan fifth order mock theta functions $\chi_0(q)$ and $\chi_1(q)$ and all three of Ramanujan's seventh order mock theta functions. We find that…

Ramanujan derived a sequence of even weight $2n$ quasimodular forms $U_{2n}(q)$ from derivatives of Jacobi's weight $3/2$ theta function. Using the generating function for this sequence, one can construct sequences of quasimodular forms of…

We prove that the coefficients of certain mock theta functions possess no linear congruences modulo 3. We prove similar results for the moduli 2 and 3 for a wide class of weakly holomorphic modular forms and discuss applications. This…

In the explicit formula for the signed mock theta functions $\Phi^{(-)[m,s]}$ obtained from the coroot lattice of $D(2,1;a)$, functions with indefinite quadratic forms naturally take place. We compute their modular transformation properties…

We formulate and prove the analogue of the Ramanujan Conjectures for modular forms of half-integral weight subject to some ramification restriction in the setting of a polynomial ring over a finite field. This is applied to give an…

In 2013, Lemke Oliver classified all eta-quotients which are theta functions. In this paper, we unify the eta-theta functions by constructing mock modular forms from the eta-theta functions with even characters, such that the shadows of…

Ramanujan's 1920 last letter to Hardy contains seventeen examples of mock theta functions which he organized into three "orders." The most famous of these is the third-order function $f(q)$ which has received the most attention of any…

Zagier's well-known work on traces of singular moduli relates the coefficients of certain weakly holomorphic modular forms of weight $1/2$ to traces of values of the modular $j$-function at imaginary quadratic points. A real quadratic…

In recent work, Hickerson and the author demonstrated that it is useful to think of Appell--Lerch sums as partial theta functions. This notion can be used to relate identities involving partial theta functions with identities involving…

We give a characterization of modified (in the sense of Zwegers) mock theta functions, parallel to that of ordinary theta functions. Namely, modified mock theta functions are characterized by their analyticity properties, elliptic…

False theta functions closely resemble ordinary theta functions, however they do not have the modular transformation properties that theta functions have. In this paper, we find modular completions for false theta functions, which among…

In this paper, we study modular transformation properties of a certain class of functions with indefinite quadratic forms.

We present q-series proofs of four identities involving sixth order mock theta functions from Ramanujan's lost notebook. We also show how Ramanujan's identities can be used to give a quick proof of four sixth order identities of Berndt and…