Papers
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The Weil bound for generalized Kloosterman sums of half-integral weight
with G. Anderson and A. Woodall, submitted.
[arxiv]
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The Shimura lift and congruences for modular forms with the eta multiplier
with S. Ahlgren and R. Dicks, submitted.
[arxiv]
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An infinite family of vector-valued mock theta functions
with C. Williams, Ramanujan J (2023).
[arxiv]
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Hybrid subconvexity and the partition function
with H. Wu, J. Number Theory 242 (2023) pp. 154--180.
[arxiv]
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Non-convex geometry of numbers and continued fractions
with W. Duke, Z. Hacking, and A. Woodall, Funct. Approx. Comment. Math., to appear.
[arxiv]
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Asymptotic distribution of traces of singular moduli
with W. Duke, Discrete Analysis 2022:4, 14 pp.
[arxiv]
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Odd, spoof perfect factorizations
with the BYU Computational Number Theory Group, J. Number Theory 234(2022), 31–47.
[arxiv]
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Zeros of GL2 L-functions on the critical line
with J. Thorner, Forum Math. 33(2021), no.2, 477–491.
[arxiv]
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On a theorem of Davenport and Schmidt
with W. Duke, Acta Arith. 198(2021), no.1, 37–75.
[arxiv]
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The Minkowski chain and Diophantine approximation
with W. Duke, J. Theor. Nombres Bordeaux 32(2020), no.2, 503–523.
[arxiv]
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Modular invariants for real quadratic fields and Kloosterman sums
with W. Duke, Algebra & Number Theory 14(2020), no.6, 1537–1575.
[arxiv]
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Markov spectra for modular billiards
with W. Duke, Math. Annalen 373 (2019), no. 3-4, 1151-1175.
[arxiv]
[journal]
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Level reciprocity in the twisted second moment of Rankin-Selberg L-functions
with E. M. Kiral, Mathematika 64 (2018), no. 3, 770-784.
[arxiv]
[journal]
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Shifted polyharmonic Maass forms for PSL(2,Z)
with J. Lagarias and R. Rhoades, Acta Arith. 185 (2018), 39-79.
[arxiv]
[journal]
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A polyharmonic Maass form of depth 3/2 for SL2(Z)
with S. Ahlgren and D. Samart, J. Math. Anal. Appl. 468 (2018), no. 2, 1018-1042.
[arxiv]
[journal]
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Images of Maass-Poincare series in the lower half-plane
with K. Bringmann and L. Rolen, L-functions and automorphic forms, Contrib. in Math. and Comp. Science 10, Springer 2017.
[arxiv]
[book]
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Vector-valued modular forms and the seventh order mock theta functions
Analytic number theory, modular forms and q-hypergeometric series, 11-23, Springer Proc. Math. Stat., 221, Springer, Cham, 2017.
[pdf]
[book]
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Vector-valued modular forms and the mock theta conjectures
Res. Number Theory (2016) 2:32.
[arxiv]
[journal]
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Kloosterman sums and Maass cusp forms of half integral weight for the modular group
with S. Ahlgren, Int. Math. Res. Notices, rnw234 (2016), 1-79.
[arxiv]
[journal]
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Algebraic and transcendental formulas for the smallest parts function
with S. Ahlgren, Adv. Math. 289 (2016) 411-437.
[arxiv]
[journal]
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Singular invariants and coefficients of weak harmonic Maass forms of weight 5/2
Forum Math. 29 (2017), no. 1, 7-29.
[arxiv]
[journal]
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Periods of the j-function along infinite geodesics and mock modular forms
Bull. Lond. Math. Soc. 47 (2015), 407-415.
[arxiv]
[journal]
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Euler-like recurrences for smallest parts functions
with S. Ahlgren, Ramanujan J. 36 (2015), special issue in memory of Basil Gordon, 237-248.
[arxiv]
[journal]
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Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function
with S. Ahlgren, Res. Number Theory (2015) 1:10.
[arxiv]
[journal]
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Classification of congruences for mock theta functions and weakly holomorphic modular forms
Q. J. Math. (2014) 65 (3): 781-805.
[arxiv]
[journal]
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Hecke grids and congruences for weakly holomorphic modular forms
with S. Ahlgren, Contemp. Math. 627 (2014).
[arxiv]
[book]
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Effective congruences for mock theta functions
with H. Friedlander, J. Fuller, H. Goodson, Mathematics (2013), 1, 100-110.
[arxiv]
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Hecke-type congruences for two smallest parts functions
Int. J. Number Theory, 09, 713-728 (2013).
[arxiv]
[journal]
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Divisibility properties of coefficients of level p modular functions for genus zero primes
with P. Jenkins, Proc. Amer. Math. Soc. 141 (2013), 41-53.
[arxiv]
[journal]
If you would like to see my thesis,
here it is, but I recommend that you look at the individual papers instead (8, 9, 11, and 12 above).
Awards and Honors
- Simons Grant, 2021-2026, award number 854098
- National Science Foundation Grant, 2017-2021, DMS-1701638 (co-PI with W. Duke)
- Plenary speaker at PANTS XXVIII (2017)
- Plenary speaker at TORA VII (2016)
- 2016 Bateman Prize (excellence in number theory research)
- Dissertation Completion Fellowship (2015-2016)
- 2015 Bateman Fellowship (excellence in number theory research)
- 2014-2016 Illinois ARCS Scholar (research grant)