Research
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​Preprints of each of my papers can be downloaded by clicking on the corresponding title. An asterisk (*) is used to denote undergraduate co-authors. 

26. Cyclotomic statistics
To appear in Essays in Analytic Number Theory -- In Honor of Helmut Maier's 70th Birthday
Edited by John Friedlander, Carl Pomerance, and Michael Th. Rassias. 

25. Sums of proper divisors with missing digits
Research Directions in Number Theory, Springer AWMS, 32, 93-110 (2024).
Joint with Kübra Benli, Giulia Cesana, Cécile Dartyge, and Charlotte Dombrowsky.

24. Summing mu(n): a faster elementary algorithm.
Research in Number Theory 9, no. 6 (2023).
Joint with Harald Andrés Helfgott.

23. Counting Salem numbers of arithmetic hyperbolic 3-orbifolds.
Bulletin of the Brazilian Mathematical Society, 53, 553–569 (2022).
Joint with Mikhail Belolipetsky, Matilde Lalín, Plinio G. P. Murillo.

22. Counting and effective rigidity in algebra and geometry. 
Mathematisches Forschungsinstitut Oberwolfach. Report No. 50/2019, pp. 55–58. 

21. The Fourier coefficients of Eisenstein series newforms.
Contemporary Mathematics, 732 (2019), 169 – 176.
Joint with Benjamin Linowitz.

20. Counting and effective rigidity in algebra and geometry.
Inventiones Mathematicae 213, no. 2 (2018), 697-758.
Joint with Benjamin Linowitz, D. B. McReynolds, Paul Pollack. 

19. Divisor-sum fibers.
Mathematika 64, no. 2 (2018), 330-342. ​ 
Joint with Paul Pollack and Carl Pomerance.

18.  Lower bounds for heights in relative Galois extensions. 
Contributions to Number Theory and Arithmetic Geometry, Springer AWMS 11 (2018), 1-17.
Joint with Kevser Aktas, Shabnam Akhtari, Kirsti Biggs, Alia Hamieh, and Kathleen Petersen. 

17. A generalization of the practical numbers.
International Journal of Number Theory 14​, no. 5 (2018), 1487-1503.
Joint with Nicholas Schwab*.

​16. Bounded gaps between primes and the length spectra of arithmetic hyperbolic 3- orbifolds.
Comptes Rendus Mathematique 355, no. 11 (2017), p. 1121-1126.
Joint with Benjamin Linowitz, D. B. McReynolds, and Paul Pollack. 

15. Systoles of arithmetic hyperbolic surfaces and 3-manifolds.
Mathematical Research Letters 24, no. 5 (2017), p. 1497-1522. 
Joint with Benjamin Linowitz, D. B. McReynolds, Paul Pollack. 

14. On integers n for which x^n − 1 has a divisor of every degree.
Acta Arithmetica 175, no. 3 (2016), p. 225-244.
Joint with Carl Pomerance and Andreas Weingartner. 

13. Arithmetic functions at consecutive shifted primes.
International Journal of Number Theory 11, no. 5 (2015), p. 1477-1498.
Joint with Paul Pollack. 

12. Bounded gaps between primes in number fields and function fields.
Proceedings of the American Mathematical Society 143 (2015), p. 2841-2856.
Joint with Abel Castillo, Chris Hall, Robert Lemke Oliver, and Paul Pollack. 

11. The sign changes of Fourier coefficients of Eisenstein series.
The Ramanujan Journal 37, no. 2 (2015), p. 223-241.
Joint with Benjamin Linowitz. 

10. Abelian surfaces with prescribed groups.
Bulletin of the London Mathematical Society 46 (2014), p. 779-792.
Joint with Chantal David, Derek Garton, Zachary Scherr, Arul Shankar, and Ethan Smith. 

9. Variations on a question concerning the degrees of divisors of x^n − 1. 
Journal de Theorie des Nombres Bordeaux 26, no. 1 (2014), p. 253-267. 

8. Variations on a theorem of Davenport concerning abundant numbers.
Bulletin of the Australian Mathematical Society 89, no. 3 (2014), p. 437-450.
Joint with Emily Jennings and Paul Pollack. 

7. Distribution of squarefree values of sequences associated with elliptic curves.
Contemporary Mathematics 606, Amer. Math. Soc. (2013), p. 171-188.
Joint with Shabnam Akhtari, Chantal David, and Heekyoung Hahn. 

6. Practical pretenders.
Publicationes Mathematicae Debrecen 82 (2013), p. 651-667.
Joint with Paul Pollack. 

5. On the degrees of divisors of T^n − 1.
New York Journal of Mathematics 19 (2013), p. 91-116.
Joint with Paul Pollack. 

4. On the divisors of x^n − 1 in Fp[x].
International Journal of Number Theory 9, no. 2 (2013), p. 421-430. 

3. On the divisors of x^n − 1. 
Electron. Notes Discrete Math. 43 (2013), p. 141–149.

2. Polynomials with divisors of every degree.
Journal of Number Theory 132 (2012), p. 1038-1053. 

1. Heights of divisors of x^n − 1.
Integers 11A. Proceedings of the Integers Conference 2009 (2011). Article 20, p. 1-9. 

0. Products of distinct cyclotomic polynomials.
Ph.D. thesis, Dartmouth College (2012).