scholarly journals The Mordell integral, quantum modular forms, and mock Jacobi forms

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
Bobbie Chern ◽  
Robert C Rhoades
Keyword(s):  
Modular Forms ◽  
Jacobi Forms ◽  
Quantum Modular Forms ◽  
Mordell Integral ◽  
Integral Quantum

scholarly journals Negative index Jacobi forms and quantum modular forms

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Kathrin Bringmann ◽  
Thomas Creutzig ◽  
Larry Rolen
Keyword(s):  
Modular Forms ◽  
Jacobi Forms ◽  
Negative Index ◽  
Quantum Modular Forms

scholarly journals Quantum modular forms and plumbing graphs of 3-manifolds

2020 ◽  
Vol 170 ◽  
pp. 105145 ◽  
Author(s):  
Kathrin Bringmann ◽  
Karl Mahlburg ◽  
Antun Milas
Keyword(s):  
Modular Forms ◽  
Quantum Modular Forms

scholarly journals On the Fourier expansions of Jacobi forms of half-integral weight

2006 ◽  
Vol 2006 ◽  
pp. 1-11
Author(s):  
B. Ramakrishnan ◽  
Brundaban Sahu
Keyword(s):  
Modular Forms ◽  
Jacobi Form ◽  
Jacobi Forms ◽  
Number Of Components ◽  
Half Integral Weight ◽  
Integral Weight ◽  
Fourier Expansions ◽  
The Given ◽  
The Relationship ◽  
Vector Valued

Using the relationship between Jacobi forms of half-integral weight and vector valued modular forms, we obtain the number of components which determine the given Jacobi form of indexp,p2orpq, wherepandqare odd primes.

scholarly journals “Strange” combinatorial quantum modular forms

2017 ◽  
Vol 170 ◽  
pp. 315-346 ◽  
Author(s):  
Amanda Folsom ◽  
Caleb Ki ◽  
Yen Nhi Truong Vu ◽  
Bowen Yang
Keyword(s):  
Modular Forms ◽  
Quantum Modular Forms

Mock modular forms and quantum modular forms

2015 ◽  
Vol 144 (6) ◽  
pp. 2337-2349 ◽  
Author(s):  
Dohoon Choi ◽  
Subong Lim ◽  
Robert C. Rhoades
Keyword(s):  
Modular Forms ◽  
Quantum Modular Forms ◽  
Mock Modular Forms

scholarly journals Torus knots and quantum modular forms

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Kazuhiro Hikami ◽  
Jeremy Lovejoy
Keyword(s):  
Modular Forms ◽  
Torus Knots ◽  
Quantum Modular Forms

ON A CORRESPONDENCE BETWEEN JACOBI CUSP FORMS AND ELLIPTIC CUSP FORMS

2013 ◽  
Vol 09 (04) ◽  
pp. 917-937 ◽  
Author(s):  
B. RAMAKRISHNAN ◽  
KARAM DEO SHANKHADHAR
Keyword(s):  
Modular Forms ◽  
Quadratic Forms ◽  
Cusp Forms ◽  
Jacobi Forms ◽  
Binary Quadratic Forms ◽  
Congruence Subgroups ◽  
Half Integral Weight ◽  
Integral Weight ◽  
Forms Of Higher Degree ◽  
Appl Math

In this paper, we prove a generalization of a correspondence between holomorphic Jacobi cusp forms of higher degree (matrix index) and elliptic cusp forms obtained by K. Bringmann [Lifting maps from a vector space of Jacobi cusp forms to a subspace of elliptic modular forms, Math. Z.253 (2006) 735–752], for forms of higher levels (for congruence subgroups). To achieve this, we make use of the method adopted by M. Manickam and the first author in Sec. 3 of [On Shimura, Shintani and Eichler–Zagier correspondences, Trans. Amer. Math. Soc.352 (2000) 2601–2617], who obtained similar correspondence in the degree one case. We also derive a similar correspondence in the case of skew-holomorphic Jacobi forms (matrix index and for congruence subgroups). Such results in the degree one case (for the full group) were obtained by N.-P. Skoruppa [Developments in the theory of Jacobi forms, in Automorphic Functions and Their Applications, Khabarovsk, 1988 (Acad. Sci. USSR, Inst. Appl. Math., Khabarovsk, 1990), pp. 168–185; Binary quadratic forms and the Fourier coefficients of elliptic and Jacobi modular forms, J. Reine Angew. Math.411 (1990) 66–95] and by M. Manickam [Newforms of half-integral weight and some problems on modular forms, Ph.D. thesis, University of Madras (1989)].

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