Publications

 

39.    Book Review: “My Search for Ramanujan” by K. Ono and A. D. Aczel, Bhavana vol. 1 iss. 2., April 2017.


38.    Perspectives on mock modular forms, Journal of Number Theory 176 (2017), 500-540.


37.    Quantum Jacobi forms and finite evaluations of unimodal rank generating functions,
         (with K. Bringmann),
Archiv der Mathematik 107 (2016), 367-378.


  1. 36.   Asymptotic behavior of partial and false theta functions arising from Jacobi forms and

         regularized characters, (with K. Bringmann and A. Milas), Journal of Mathematical Physics
         58 011702 (2017), 19pp.

  1. 35.   Quantum mock modular forms arising from eta-theta functions, (with S. Garthwaite, S-Y Kang,
       H. Swisher, and S. Treneer),
    Research in Number Theory 2:14 (2016), 41pp.              


34.    Mock and mixed mock modular forms in the lower half-plane, Archiv der Mathematik 107
        (2016), 487-498.


33.    Zeros of modular forms of half integral weight, (with P. Jenkins), Research in Number Theory
       
2:23 (2016), 25pp.

32.   Strange combinatorial quantum modular forms, (with C. Ki, Y.N. Truong Vu, and B. Yang),
       
Journal of Number Theory 170 (2017), 315-346.


31.   On a general class of non-squashing partitions, (with Y. Homma, J. Ryu, and B. Tong),

        Discrete Mathematics 339 iss. 5 (2016), 1482-1506.


30.   Conic theta functions and their relations to theta functions, (with W. Kohnen and S. Robins).
       
Annales de l’Institut Fourier (Grenoble) 65 no. 3 (2015), 1133-1151.


29.   Unimodal sequences and “strange” functions:  a family of quantum modular forms,

        (with K. Bringmann and R.C. Rhoades).

        Pacific Journal of Mathematics 274 no. 1 (2015), 1-25.


28.  Ramanujan's radial limits, (with K. Ono and R.C. Rhoades).
        Contemporary Mathematics 627, Ramanujan 125, ed. K. Alladi, F. Garvan, and A.J. Yee,

        American Mathematical Society (2014).


27.  Recent work on the partition function, (with J. Bruinier, Z. Kent, and K. Ono).

        Ramanujan Mathematical Society Lecture Notes 20 (2013), ed. B.C. Berndt and D. Prasad, 139-151.


26.   Mock modular forms and d-distinct partitions.
        Advances in Mathematics 254 (2014), 682-705.

25.   Mock theta functions and quantum modular forms, (with K. Ono and R.C. Rhoades).
        Forum of Mathematics Pi 1 (2013), 1-27.

24.   Almost harmonic Maass forms and Kac-Wakimoto characters, (with K. Bringmann).
        Journal für die reine und angewandte Mathematik (Crelle's Journal) 694 (2014), 179-202.

23.   Graded dimensions of principal subspaces and modular Andrews-Gordon series,

        (with K. Bringmann, C. Calinescu, and S. Kimport).
        Communications in Contemporary Mathematics 16 no. 4 (2014), 1350050 [20 pages].


22.   Mock modular forms and singular combinatorial series, (with S. Kimport).   
        Acta Arithmetica 159.3 (2013), 257-297.

21.   Quasimodular forms and sl(m|m)^ characters, (with K. Bringmann and K. Mahlburg).
        Ramanujan Journal, Gordon memorial volume 36 (2015), 103-116.

20.   l-adic properties of the partition function, (with Z. Kent, K. Ono).
        Advances in Mathematics 229 (2012), 1586-1609.

  1. 19.  Partial theta functions and mock modular forms as q-hypergeometric series, (with K. Bringmann,

        R.C. Rhoades). Ramanujan Journal, special issue Ramanujan's 125th birthday, 29 (2012), 295-310.

18.   The probability that the number of points on the Jacobian of a genus 2 curve is prime,

        (with W. Castryck, H. Hubrechts, A.V. Sutherland).
        Proceedings of the London Mathematical Society, (3) 104 (2012), 1235-1270.

17.   On a conjecture of B. Berndt and B. Kim, (with K. Bringmann).
        Ramanujan Journal 32 (2013), 1-4.

16.  On the asymptotic behavior of Kac-Wakimoto characters, (with K. Bringmann).
       Proceedings of the American Mathematical Society 141 no. 5 (2013), 1567-1576.

15.  WHAT IS...a mock modular form?
       Notices of the American Mathematical Society 57 issue 11 (2010), 1441-1443.

14.  Kac-Wakimoto characters and universal mock theta functions.
       Transactions of the American Mathematical Society 363 no. 1 (2011), 439-455.

13.  Modularity and the distinct rank function.
       Ramanujan Journal, George Andrews birthday edition, 23 nos. 1-3 (2010), 183-193.

12.  Book Review: The 1-2-3 of modular forms, by J.H. Bruinier, G. van der Geer, G. Harder, and D. Zagier.
       Bulletin of the American Mathematical Society 46 (2009), 527-533.

11.  The asymptotic distribution of traces of Maass-Poincaré series, (with R. Masri).
       Advances in Mathematics 226 (2011), 3724-3759.

10.  Equidistribution of Heegner points and the partition function, (with R. Masri).
       Mathematische Annalen 348 no. 2 (2010), 289-317.

9.   The spt-function of Andrews, (with K. Ono).

      (Note. Thm. 1.2 should be stated for p^(4a+1)m^2, (p,m)=1, instead of pm^2.)
      Proceedings of the National Academy of Sciences, USA, 105 no. 51 (2008), 20152-20156.

8.   A short proof of the mock theta conjectures using Maass forms.
      Proceedings of the American Mathematical Society 136 (2008), 4143-4149.

7.   q-series and weight 3/2 Maass forms, (with K. Bringmann, K. Ono).
      Compositio Mathematica 145 (2009), 541-552.

6.   Duality involving the mock theta function f(q), (with K. Ono).
      Journal of the London Mathematical Society (2) 77 (2008), 320-334.
      Corrigendum. (Some numbers in Table (1.3) are corrected.)

5.   Modular units and the q-difference equations of Selberg.
      Mathematical Research Letters (17) no. 2 (2010), 283-299.

4.  Class invariants and cyclotomic unit groups from special values of modular units.
     Journal de Théorie des Nombres de Bordeaux (20) no. 2 (2008), 289-325.

3.  A characterization of the modular units.
     International Journal of Number Theory (5) no. 2 (2009), 303-310.

2.  Modular forms and Eisenstein's continued fractions.
     Journal of Number Theory 117 Issue 2 (2006), 279-291.

  1. 1. On a quantitative refinement of the Lagrange spectrum, (with E. Burger, A. Pekker, R. Roengpitya,

     J. Snyder).  Acta Arithmetica 102.1 (2002), 55-82.

Book:      Harmonic Maass forms and mock modular forms: theory and applications (with K. Bringmann, K. Ono, L. Rolen).

                 AMS Colloquium Series, (submitted 12/2016). 

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