Harmonic Maass Forms and Mock Modular Forms: Theory and Applications

The asymptotic profile of an eta-theta quotient related to entanglement entropy in string theory

“…For a fixed value of z the problem of finding the asymptotics of the coefficients is elementary, as [12] notes. In particular, fixing z = h k a rational number with gcd(h, k) = 1 and 0 ≤ h < k 2 , then classical results in the theory of modular forms (see Theorem 15.10 of [3] for example) give that the coefficients of f ( h k ; τ ) = n≥0 a h,k (n)q n behave asymptotically as…”

On Weierstrass mock modular forms and a dimension formula for certain vertex operator algebras

“…as the classical Petersson scalar product. With this we have the following important result (see [7,Proposition 5.10]), which follows essentially from an application of Stokes's Theorem.…”

“…In this section, we briefly recall some basic definitions and facts about mock modular forms and harmonic Maaß forms. For more detailed information as well as references to original works, the reader may consult for example the book [7].…”

“…These functions naturally split into a holomorphic and a non-holomorphic part [7,Lemma 4.3], f = f + + f − . The holomorphic part of a harmonic Maaß form is called a mock modular form.…”

“…The non-holomorphic part of a harmonic Maaß form is related to a cusp form called the shadow of the corresponding mock modular form [7,Theorem 5.10].…”