Half-integral weight Eichler integrals and quantum modular forms

Bringmann, Kathrin; Rolen, Larry

doi:10.1016/j.jnt.2015.03.001

Cited by 29 publications

(41 citation statements)

References 20 publications

(26 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…4. As argued in [4,6,13,29,30], for example, the integrals appearing in parts (i) and (ii) of Theorem 1.2 are real analytic functions, except at −1/2 and −1 (respectively). …”

Section: Proof Ofmentioning

confidence: 82%

“…2.3. In the example given above in (4), it turns out that the shadow of Ramanujan's q-hypergeometric mock theta function is essentially the modular theta function given in the numerator of the integral appearing there (up to a simple multiplicative factor).…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

“…1, these functions may be viewed as formal Eichler integrals of the modular eta-theta functions E m , or, as partial theta functions. Connections between these types of functions and mock modular and quantum modular forms have been explored in a number of works, including [4,12,13,19,29,30].…”

Section: Lemma 21 For All γ = a Bmentioning

confidence: 99%

See 2 more Smart Citations

Quantum mock modular forms arising from eta–theta functions

et al. 2016

View full text Add to dashboard Cite

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.

show abstract

“…4. As argued in [4,6,13,29,30], for example, the integrals appearing in parts (i) and (ii) of Theorem 1.2 are real analytic functions, except at −1/2 and −1 (respectively). …”

Section: Proof Ofmentioning

confidence: 82%

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Quantum mock modular forms arising from eta–theta functions

et al. 2016

View full text Add to dashboard Cite

show abstract

“…S k (2)) is equal to the space of modular forms (resp. cusp forms) of weight k for H (2), as explained at the end of Sect. This proves our assertion.…”

Section: Theorem 4 Under the Given Hypotheses The Following Assertiomentioning

confidence: 99%

“…In [2], Bringmann and Rolen used the function E nh f (z) to study the asymptotic expansion for t → 0 of certain power series in t whose coefficients are given by special values of L f (s) (and twists of the latter by additive characters) at half-integral points s = k − 1 − n with n ∈ N 0 . This had an important implication regarding the construction of quantum modular forms attached to f in the sense of Zagier.…”

Section: Introductionmentioning

confidence: 99%