Publications and Preprints
Regular ternary polygonal forms (with Zilong He)
Ramanujan J., accepted for publication.
An extension of Rohrlich's Theorem to the j-function (with Kathrin Bringmann)
Forum Math. Sigma 8, e3, 1-33. DOI: 10.1017/fms.2019.46
- Central L-values of elliptic curves and local polynomials (with Stephan Ehlen, Pavel Guerzhoy, and Larry Rolen)
Proc. London Math. Soc. 120 (2020), 742-769.
Interesting identities involving weighted representations of integers as sums of arbitrarily many squares (with Min-Joo Jang, Winfried Kohnen, and Siu Hang Man)
Proc. Natl. Acad. Sci (USA) 116, issue 39 (2019), 19374-19379. DOI: http://doi.org/10.1073/pnas.1906632116
Differential operators on polar harmonic Maass forms and elliptic duality (with Kathrin Bringmann and Paul Jenkins)
Q. J. Math. 70 (2019), 1181-1207, DOI: 10.1093/qmath/haz009.
Universal sums of m-gonal numbers (with Jingbo Liu)
Int. Math. Res. Not., accepted for publication, DOI: 10.1093/imrn/rnz003.
Regularized inner products of meromorphic modular forms and higher Green's functions (with Kathrin Bringmann and Anna-Marie von Pippich)
Commun. Contemp. Math. 21 (2019), 1850029.
On divisors of modular forms (with Kathrin Bringmann, Steffen Löbrich, Ken Ono, and Larry Rolen)
Adv. Math. 329 (2018), 541-554. Corrigendum: DOI 10.1016/j.aim.2019.106751.
Almost universal ternary sums of polygonal numbers (with Anna Haensch)
Research in Number Theory 4:4 (2018), 1-22.
Regularized inner products and weakly holomorphic Hecke eigenforms (with Kathrin Bringmann)
Journal of Physics A: Mathematical and Theoretical 51 (2018) 044001.
- The Bruinier--Funke pairing and the orthogonal complement of unary theta functions (with Siu Hang Man) (local version)
in Bruinier, J., Kohnen, W. (Eds.), "L-functions and automorphic forms",
Contributions in mathematical and computational sciences 10 (2017), Springer, 139-157.
On the Andrews-Zagier asymptotics for partitions without sequences (alternative link here) (with Kathrin Bringmann, Dan Parry, and Rob Rhoades)
Adv. Math. 309 (2017), 436-451.
- Analogues of the Ramanujan--Mordell Theorem (with Shaun Cooper and Dongxi Ye)
J. Math. Anal. Appl. 446 (2017), 568-579.
- On sign changes of cusp forms and the halting of an algorithm to construct a supersingular elliptic curve with a given endomorphism ring (with King Cheong Fung)
Math. Comp. 87 (2017), 501-514.
Polar harmonic Maass forms and their applications (with Kathrin Bringmann)
Abh. Math. Sem. Univ. Hamburg 86 (2016), 213-233.
A problem of Petersson about weight 0 meromorphic modular forms (with Kathrin Bringmann)
Res. Math. Sci. 3:24 (2016), 1-31.
- Ramanujan and coefficients of meromorphic modular forms (with Kathrin Bringmann)
J. Math. Pures Appl. 107 (2017), 100-122.
- Explicit congruences for mock modular forms (with Matthias Waldherr)
J. Number Theory 166 (2016), 1-18.
Half-integral weight p-adic coupling of weakly holomorphic and holomorphic modular forms
(with Kathrin Bringmann and Pavel Guerzhoy)
Research in Number Theory 1:26 (2015), 1-13.
On cycle integrals of weakly holomorphic modular forms (with Kathrin Bringmann and Pavel Guerzhoy)
Math. Proc. Cambridge Philos. Soc. 158 (2015), 439-449.
Modular local polynomials (with Kathrin Bringmann)
Math. Res. Lett. 23 (2016), 973-986.
Locally harmonic Maass forms and the kernel of the Shintani lift (local version) (with Kathrin Bringmann and Winfried Kohnen)
Int. Math. Res. Not. 2015 (2015), 3185-3224.
Shintani lifts and fractional derivatives for harmonic weak Maass forms (with Kathrin Bringmann and Pavel Guerzhoy)
Adv. Math. 255 (2014), 641-671.
Sums of class numbers and mixed mock modular forms (with Kathrin Bringmann),
Math. Proc. Cambridge Philos. Soc. 167 (2019), 321-333. DOI: 10.1017/S030500411800034.
Theta lifts and local Maass forms (with Kathrin Bringmann and Maryna Viazovska),
Math. Res. Lett. 20 (2013), 213-234.
On a completed generating function of locally harmonic Maass forms (with Kathrin Bringmann and Sander Zwegers),
Compositio Math. 150 (2014), 749-762, doi:10.1112/S0010437X13007719.
- Second order cusp forms and mixed mock modular forms (with Kathrin Bringmann),
Ramanujan J., Special issue in honor of Ismail and Stanton, 31 (2013), 147-161, doi: 10.1007/s11139-012-9408-4.
- Duality and differential operators for harmonic Maass forms (with Kathrin Bringmann and Robert Rhoades)
Dev. Math. 28, Special volume in memory of Leon Ehrenpreis: From Fourier analysis and number theory to radon transforms and geometry (2013), 85-106, doi: 10.1007/978-1-4614-4075-8_6.
- Inequalities for full rank differences of 2-marked Durfee symbols (with Kathrin Bringmann)
J. Combin. Theory Ser. A 119 (2012), 483-501.
- The triangular theorem of eight and representation by quadratic polynomials (with Wieb Bosma),
Proc. Amer. Math. Soc. 141 (2013), 1473-1486.
- Faber polynomials and Poincaré series,
Math. Res. Lett. 18, no. 4 (2011), 591-611.
- Mock modular forms as $p$-adic modular forms (with Kathrin Bringmann and Pavel Guerzhoy),
Trans. Amer. Math. Soc. 364 (2012), 2393-2410.
- Equidistribution of Heegner Points and Ternary Quadratic Forms (with Dimitar Jetchev),
Math. Ann. 350, no. 3 (2011), 501-532.
- The aliquot constant (with Wieb Bosma),
Q. J. Math 63, no. 2 (2012), 309-323.
- Representing sets with sums of triangular numbers,
Int. Math. Res. Not. 2009, no. 17 (2009), 3264-3285, doi:10.1093/imrn/rnp053.
- On almost universal mixed sums of squares and triangular numbers (with Zhi-Wei Sun),
Trans. Amer. Math. Soc. 362 (2010), 6425-6455.
- Multiplicative $q$-hypergeometric series arising from real quadratic fields (with Kathrin Bringmann),
Trans. Amer. Math. Soc. 363 (2011), 2191-2209.
- Inequalities for differences of Dyson's rank for all odd moduli (with Kathrin Bringmann),
Math. Res. Lett. 17, no. 5 (2010), 927-942.
- New identities involving sums of the tails related to real quadratic fields (with Kathrin Bringmann),
Special issue of the Ramanujan J. in honor of G.E. Andrews's 70th birthday, The Ramanujan J. 23 (2010), 243-251.
- CM liftings of supersingular elliptic curves,
J. Théor. Nombres Bordeaux 21, no. 3 (2009), 635-663.
- Representations of integers by ternary quadratic forms,
Int. J. Number Theory 6, no. 1 (2010), 127-158.
- On simultaneous $s$-cores/$t$-cores (with David Aukerman and Lawrence Sze),
Discrete Math. 309 (2009), 2712-2720.
- On two conjectures about mixed sums of squares and triangular numbers,
J. Comb. Number Theory 1, no. 1 (2009), 77-90.
- Sums of triangular numbers and $t$-core partitions,
J. Comb. Number Theory 1, no. 1 (2009), 59-64.
- On the boundary behaviour of automorphic forms (with Kathrin Bringmann and Winfried Kohnen)
Int. J. Number Theory 2, no. 2 (2006), 187-194.
Expository notes/survey papers:
Sign changes of Fourier coefficients of cusp forms of half-integral weight over split and inert primes in quadratic number fields (with Zilong He)
submitted for publication.
Class numbers and representations by ternary quadratic forms with congruence conditions (with Kathrin Bringmann)
submitted for publication. GP/Pari code created for this project may be found here.
Fermat's polygonal number theorem for repeated generalized polygonal numbers (with Soumyarup Banerjee, Manav Batavia, Muratzhan Kyranbay, Dayoon Park, Sagnik Saha, Hiu Chun So, and Piyush Varyani)
submitted for publication.
Ramanujan-like formulas for Fourier coefficients of all meromorphic cusp forms (with Kathrin Bringmann)
submitted for publication.
Regularized Petersson inner products for meromorphic modular forms
Proceedings of RIMS (Surikaisekikenkyusho 2036) Kokyuroku conference "Automorphic forms, automorphic L-functions, and related topics" held at RIMS in February, 2016, (2017), 20-30.
Topical review: Number theoretic generalization of the Monster denominator formula (with Kathrin Bringmann, Steffen Löbrich, Ken Ono, and Larry Rolen)
Journal of Physics A: Mathematical and Theoretical 50 (2017) 473001.
Polar harmonic Maass forms
Book chapter in "Encyclopedia of Srinivasa Ramanujan and His Mathematics", 3 pages, 2017.
An algebraic and analytic approach to spinor exceptional behavior in translated lattices (with Anna Haensch), Conference Proceedings of the 3rd Building Bridges Workshop 11—22 July, 2016, AMS Contemporary Mathematics series, to appear.
The Monster denominator formula
Book chapter in "Encyclopedia of Srinivasa Ramanujan and His Mathematics", in preparation.