Amanda Folsom

Bicentennial Professor of Mathematics

Amherst College
Department of Mathematics and Statistics
Amherst, MA 01002





I. Books

  1. Co-Author of:
    K. Bringmann, A. Folsom, K. Ono, and L. Rolen,
    Harmonic Maass forms and mock modular forms: theory and applications, AMS Colloquium Publications, 64. American Mathematical Society, Providence, RI, 2018.  391pp.  (Errata .pdf)









II. Research Articles


  1. A. Folsom, Periodic partial theta functions and q-hypergeometric knot multi sums as quantum Jacobi forms, preprint 2023. 27pp.
  2. A. Folsom, J. Males, and L. Rolen, Equidistribution and partition polynomials, submitted 2022. 15pp.
  3. C. Ballantine and A. Folsom, On the number of parts in all partitions enumerated by the Rogers-Ramanujan identities, submitted for publication 2022. 16pp.
  4. C. Ballantine, H. Burson, A. Folsom, C-Y Hsu, I. Negrini, and B. Wen, Mock theta functions and related combinatorics, submitted for publication 2022. 28pp.
  5. A.M. Dietrich, A. Folsom, K. Ng, C. Stewart, and S. Xu, Overpartition ranks and quantum modular forms, Research in Number Theory 8:45 (2022). 16pp.
  6. C. Ballantine, H. Burson, A. Folsom, C-Y Hsu, I. Negrini, and B. Wen, On a Partition Identity of Lehmer, Discrete Mathematics 345 (2022). 26pp.
  7. A. Folsom, E. Pratt, N. Solomon, and A.R. Tawfeek, Quantum Jacobi forms and sums of tails identities, Research in Number Theory, 8:8 (2022). 24pp.
  8. A. Folsom, Asymptotic expansions, partial theta functions, and radial limit differences of mock modular and modular forms, International Journal of Number Theory, Vol. 17, No. 2 (2021) 425–434.
  9. A. Folsom, Twisted Eisenstein series, cotangent-zeta sums, and quantum modular forms, Transactions of the London Mathematical Society, 7(1) 2020, 33-48.
  10. A. Folsom, Quantum Jacobi forms in number theory, topology, and mathematical physics, Research in the Mathematical Sciences 6:25 (2019). 34pp.
  11. A. Folsom, M-J Jang, S. Kimport, and H. Swisher, Quantum modular forms and singular combinatorial series with repeated roots of unity, Acta Arithmetica 194.4 (2020), 393-421.
  12. G. Carroll, J. Corbett, A. Folsom, and E. Thieu, Universal mock theta functions as quantum Jacobi forms, Research in the Mathematical Sciences 6:6 (2019), 15pp.
  13. M. Barnett, A. Folsom, and W.J. Wesley, Rank generating functions for odd-balanced unimodal sequences, quantum Jacobi forms and mock Jacobi forms, Journal of the Australian Mathematical Society, 109 (2020), 157-175.
  14. A. Folsom, M-J Jang, S. Kimport, and H. Swisher, Quantum modular forms and singular combinatorial series with distinct roots of unity, Springer Research Directions in Number Theory: Women in  Numbers IV.  Association for Women in Mathematics Series, vol. 19. Springer, 2019. 173-195.
  15. M. Barnett, A. Folsom, O. Ukogu, W.J. Wesley, and H. Xu, Quantum Jacobi forms and balanced unimodal sequences, Journal of Number Theory 186 (2018), 16-34.
  16. K. Bringmann and A. Folsom, Quantum Jacobi forms and finite evaluations of unimodal rank generating functions, Archiv der Mathematik 107 (2016), 367-378.
  17. K. Bringmann, A. Folsom, and A. Milas, Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters, Journal of Mathematical Physics 58 011702 (2017), 19pp.
  18. A. Folsom, S. Garthwaite, S-Y Kang, H. Swisher, and S. Treneer, Quantum mock modular forms arising from eta-theta functions, Research in Number Theory 2:14 (2016), 41pp.
  19. A. Folsom, Mock and mixed mock modular forms in the lower half-plane, Archiv der Mathematik 107 (2016), 487-498.
  20. A. Folsom and P. Jenkins, Zeros of modular forms of half integral weight,Research in Number Theory 2:23 (2016), 25pp.
  21. A. Folsom, C. Ki, Y.N. Truong Vu, and B. Yang, Strange combinatorial quantum modular forms, Journal of Number Theory 170 (2017), 315-346.
  22. A. Folsom, Y. Homma, J. Ryu, and B. Tong, On a general class of non-squashing partitions, Discrete Mathematics 339 iss. 5 (2016), 1482-1506.
  23. A. Folsom, S. Robins, and W. Kohnen, Conic theta functions and their relations to theta functions, Annales de l’Institut Fourier (Grenoble) 65 no. 3 (2015), 1133-1151.
  24. K. Bringmann, A. Folsom, and R.C. Rhoades, Unimodal sequences and “strange” functions:  a family of quantum modular forms, Pacific Journal of Mathematics 274 no. 1 (2015), 1-25.
  25. A. Folsom, K. Ono, and R.C. Rhoades, Ramanujan's radial limits, Contemporary Mathematics 627, Ramanujan 125, American Mathematical Society (2014).
  26. A. Folsom, Mock modular forms and d-distinct partitions, Advances in Mathematics 254 (2014), 682-705.
  27. A. Folsom, K. Ono, and R.C. Rhoades, Mock theta functions and quantum modular forms, Forum of Mathematics Pi 1 (2013), 1-27.
  28. K. Bringmann and A. Folsom, Almost harmonic Maass forms and Kac-Wakimoto characters, Journal für die reine und angewandte Mathematik (Crelle's Journal) 694 (2014), 179-202.
  29. K. Bringmann, C. Calinescu, A. Folsom, and S. Kimport, Graded dimensions of principal subspaces and modular Andrews-Gordon series, Communications in Contemporary Mathematics 16 no. 4 (2014), 1350050 [20 pages].
  30. A. Folsom and S. Kimport, Mock modular forms and singular combinatorial series, Acta Arithmetica 159.3 (2013), 257-297.
  31. K. Bringmann, A. Folsom, and K. Mahlburg, Quasimodular forms and sl(m|m)^ characters,Ramanujan Journal, Gordon memorial volume 36 (2015), 103-116.
  32. A. Folsom, Z. Kent, and K. Ono, l-adic properties of the partition function, Advances in Mathematics 229 (2012), 1586-1609.
  33. K. Bringmann, A. Folsom, and R.C. Rhoades, Partial theta functions and mock modular forms as q-hypergeometric series, Ramanujan Journal, special issue Ramanujan's 125th birthday, 29 (2012), 295-310.
  34. W. Castryck, A. Folsom, H. Hubrechts, and A.V. Sutherland, The probability that the number of points on the Jacobian of a genus 2 curve is prime, Proceedings of the London Mathematical Society, (3) 104 (2012), 1235-1270.
  35. K. Bringmann and A. Folsom, On a conjecture of B. Berndt and B. Kim, Ramanujan Journal 32 (2013), 1-4.
  36. K. Bringmann and A. Folsom, On the asymptotic behavior of Kac-Wakimoto characters, Proceedings of the American Mathematical Society 141 no. 5 (2013), 1567-1576.
  37. A. Folsom, Kac-Wakimoto characters and universal mock theta functions, Transactions of the American Mathematical Society 363 no. 1 (2011), 439-455.
  38. A. Folsom, Modularity and the distinct rank function. Ramanujan Journal, George Andrews birthday edition, 23 nos. 1-3 (2010), 183-193.
  39. A. Folsom and R. Masri, The asymptotic distribution of traces of Maass-Poincaré series, Advances in Mathematics 226 (2011), 3724-3759.
  40. A. Folsom and R. Masri, Equidistribution of Heegner points and the partition function, Mathematische Annalen 348 no. 2 (2010), 289-317.
  41. A. Folsom and K. Ono, The spt-function of Andrews, (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.
  42. A. Folsom, A short proof of the mock theta conjectures using Maass forms, Proceedings of the American Mathematical Society 136 (2008), 4143-4149.
  43. K. Bringmann, A. Folsom, and K. Ono, q-series and weight 3/2 Maass forms, Compositio Mathematica 145 (2009), 541-552.
  44. A. Folsom and K. Ono, Duality involving the mock theta function f(q), Corrigendum. (Some numbers in Table (1.3) are corrected.) Journal of the London Mathematical Society (2) 77 (2008), 320-334.
  45. A. Folsom, Modular units and the q-difference equations of Selberg, Mathematical Research Letters (17) no. 2 (2010), 283-299.
  46. A. Folsom, 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.
  47. A. Folsom, A characterization of the modular units, International Journal of Number Theory (5) no. 2 (2009), 303-310.
  48. A. Folsom, Modular forms and Eisenstein's continued fractions, Journal of Number Theory 117 Issue 2 (2006), 279-291.
  49. E. Burger, A. Folsom, A. Pekker, R. Roengpitya, and J. Snyder, On a quantitative refinement of the Lagrange spectrum, Acta Arithmetica 102.1 (2002), 55-82.


III. Expository Articles


  1. R. Buckmire, A. Folsom, C. Goff, A. Hoover, J. Nakao, and K. Sather-Wagstaff, On Best Practices for the Recruitment, Retention, and Flourishing of LGBTQ+ Mathematicians, submitted. 7 pp.
  2. A. Folsom and A. Kontorovich, Advice for the campus interview, Notices of the American Mathematical Society, vol. 66, no. 10, November 2019, 1651-1655.
  3. A. Folsom, Asymptotics and Ramanujan’s mock theta functions: then and now, Philosophical Transactions of the Royal Society A, 378 no. 2163, (2020), 13pp.
    *Note. This article is largely expository, but does contain one new result.
  4. A. Folsom and S. Payne, Research with undergraduates, Notices of the American Mathematical Society, vol. 66, no. 2, February 2019, 199-200.
  5. A. Folsom, Symmetry, almost, Notices of the American Mathematical Society, vol. 66, no. 1, January 2019, 87-88.
  6. A. Folsom, Harmonic Maass forms and mock modular forms,  Submitted.
  7. A. Folsom, False theta functions and modular forms,  Submitted.
  8. A. Folsom, Quantum modular forms,  Submitted.
  9. A. Folsom, A Century of Answering the Question:  What Is a Mock Theta Function,  Submitted.
  10. H-C Chan and A. Folsom, Evaluations of the Rogers-Ramanujan Continued Fraction,  Submitted.
  11. A. Folsom, Book Review: “My Search for Ramanujan” by K. Ono and A. D. Aczel, Bhavana vol. 1 iss. 2, April 2017.
  12. A. Folsom, Perspectives on mock modular forms, Journal of Number Theory 176 (2017), 500-540.
  13. J. Bruinier, A. Folsom, Z. Kent, and K. Ono, Recent work on the partition function, Ramanujan Mathematical Society Lecture Notes 20 (2013), ed. B.C. Berndt and D. Prasad, 139-151.
  14. A. Folsom, WHAT IS...a mock modular form?, Notices of the American Mathematical Society 57 issue 11 (2010), 1441-1443.
  15. A. Folsom, 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.