212 research outputs found
Mock Jacobi forms in basic hypergeometric series
We show that some -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 points and multiplied by suitable powers of . And we
prove that certain linear sums of -series are weakly holomorphic modular
forms of weight 1/2 due to annihilation of mock Jacobi forms or completion by
mock Jacobi forms. As an application, we obtain a relation between the rank and
crank of a partition.Comment: 13 page
Exact formulas for traces of singular moduli of higher level modular functions
Zagier proved that the traces of singular values of the classical j-invariant
are the Fourier coefficients of a weight 3/2 modular form and Duke provided a
new proof of the result by establishing an exact formula for the traces using
Niebur's work on a certain class of non-holomorphic modular forms. In this
short note, by utilizing Niebur's work again, we generalize Duke's result to
exact formulas for traces of singular moduli of higher level modular functions.Comment: 8 page
Quantum mock modular forms arising from eta-theta functions
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 these mock modular forms are given by the eta-theta functions with odd
characters. In addition, we prove that our mock modular forms are quantum
modular forms. As corollaries, we establish simple finite hypergeometric
expressions which may be used to evaluate Eichler integrals of the odd
eta-theta functions, as well as some curious algebraic identities.Comment: 33 page
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