I am an associate professor at
BYU.
From 2016 to 2019 I was an assistant adjunct professor (postdoc) at
UCLA.
During the Spring semester 2017 I was a postdoctoral research associate at
MSRI in the
Analytic Number Theory program.
I received my PhD in 2016 from
UIUC under the direction of
Scott Ahlgren.
I completed my BS in mathematics with a minor in physics in 2011 at
BYU.
My research interests are in number theory.
I am particularly interested in arithmetic aspects of automorphic forms and their relation to (in no particular order) invariants of quadratic number fields, hyperbolic geodesics, class numbers,
L-functions, and additive number theory.
Here is my CV.
Contact:
nick [at] math [dot] byu [dot] edu
Office 328 TMCB
Selected Papers
-
Asymptotic distribution of traces of singular moduli (with W. Duke)
submitted.
[arxiv]
-
Zeros of GL2 L-functions on the critical line (with J. Thorner)
Forum Math., to appear.
[arxiv]
-
On a theorem of Davenport and Schmidt (with W. Duke)
Acta Arith., to appear.
[arxiv]
-
The Minkowski Chain and Diophantine approximation (with W. Duke)
J. Theor. Nombres Bordeaux, to appear.
[arxiv]
-
Modular invariants for real quadratic fields and Kloosterman sums (with W. Duke)
Algebra & Number Theory, to appear.
[arxiv]
-
Markov spectra for modular billiards (with W. Duke)
Math. Annalen 373 (2019), no. 3-4, 1151-1175.
[arxiv]
[journal]
-
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]
-
Shifted polyharmonic Maass forms for PSL(2,Z) (with J. Lagarias and R. Rhoades)
Acta Arith. 185 (2018), 39-79.
[arxiv]
[journal]
-
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]
-
Vector-valued modular forms and the mock theta conjectures
Res. Number Theory (2016) 2:32.
[arxiv]
[journal]
-
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]
-
Algebraic and transcendental formulas for the smallest parts function (with S. Ahlgren)
Adv. Math. 289 (2016) 411-437.
[arxiv]
[journal]
-
Singular invariants and coefficients of weak harmonic Maass forms of weight 5/2
Forum Math. 29 (2017), no. 1, 7-29.
[arxiv]
[journal]
-
Periods of the j-function along infinite geodesics and mock modular forms
Bull. Lond. Math. Soc. 47 (2015), 407-415.
[arxiv]
[journal]
-
Classification of congruences for mock theta functions and weakly holomorphic modular forms
Q. J. Math. (2014) 65 (3): 781-805.
[arxiv]
[journal]
You can find a complete list of papers
here.
Teaching
In Winter 2020 I am teaching Math 290: Fundamentals of Mathematics and Math 371: Introduction to Abstract Algebra. I am also supervising a Python programming lab [Fall Labs] [Winter Labs] See the teaching page for my previous teaching.