Publications

48

Convergence of Fourier-Bohr coefficients
for regular Euclidean model sets (with M. Baake), chapter, Aperiodic order, Volume 3, to appear.

Preprint

47

Expected value of the smallest denominator in a random interval of fixed
radius (with H. Chen), Int. J. Number Theory, to appear.

46

A three gap theorem for the adeles (with A. Das), Ramanujan J. 60 (2023), no.1, 13-25.

45

A five distance theorem for Kronecker sequences (with J. Marklof), Int. Math. Res. Not., Int. Math. Res. Not. IMRN 2022, no.24, 19747-19789.

44

Level spacing statistics for the multi-dimensional quantum harmonic oscillator: algebraic case (with R. Roeder), J. Math. Phys. 63 (2022), no. 1, Paper No. 012102.

43

Bounded remainder sets for rotations on higher dimensional adelic tori (with A. Das, J. Furno), Mosc. J. Comb. Number Theory 10 (2021), no. 2, 111–120.

42

Badly approximable points for diagonal approximation in solenoids (with H. Chen), Acta Arith. 199 (2021), no. 2, 153–161.

41

Higher dimensional gap theorems for the maximum metric (with J. Ramirez), Int. J. Number Theory 17 (2021), no. 7, 1665–1670.

40

Higher dimensional Steinhaus and Slater problems via homogeneous dynamics (with J. Marklof), Ann. Sci. Ec. Norm. Super. 53 (2020), 537-557.

39

Higher moments of distances between consecutive Ford spheres (with K. Measures), J. Number Theory 212 (2020), pp. 88-104.

38

Sums of reciprocals of fractional parts and multiplicative Diophantine approximation (with V. Beresnevich, S. Velani), Mem. Amer. Math. Soc. 263 (2020), no. 1276.

37

Bounded remainder sets for rotations on the Adelic torus (with J. Furno, H. Koivusalo), Proc. Amer. Math. Soc. 147 (2019), no. 12, 5105–5115.

36

Statistics of patterns in typical cut and projects sets (with A. Julien, H. Koivusalo, J. Walton), Ergodic Theory Dynam. Systems 39 (2019), no. 12, 3365–3387.

35

A measure theoretic result for approximation by Delone sets (with M. Baake), Horizons of fractal geometry and complex dimensions, 35–40, Contemp. Math., 731, Amer. Math. Soc., Providence, RI, 2019.

34

A characterization of linearly repetitive cut and project sets (with H. Koivusalo, J. Walton), Nonlinearity 31 (2018), no. 2, 515–539.

33

Perfectly ordered quasicrystals and the Littlewood Conjecture (with H. Koivusalo, J. Walton), Trans. Amer. Math. Soc. 370 (2018), no. 7, 4975–4992.

32

Averaging almost periodic functions along exponential sequences (with M. Baake, D. Lenz), Aperiodic order. Vol. 2, 343–362, Encyclopedia Math. Appl., 166, Cambridge Univ. Press, Cambridge, 2017.

31

A randomized version of the Littlewood conjecture (with H. Koivusalo), J. Number Theory 178 (2017), 201-207.

30

Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices, II (with M. Kelly, H. Koivusalo), Indag. Math. 28 (2017), 138-144.

29

Gaps problems and frequencies of patches in cut and project sets (with H. Koivusalo, L. Sadun, J. Walton), Math. Proc. Cambridge Philos. Soc. 161 (2016), no. 1, 65-85.

28

Open problems and conjectures related to the theory of mathematical quasicrystals (with F. Adiceam, D. Damanik, F. Gahler, U. Grimm, A. Julien, A. Navas, L. Sadun, B. Weiss), Arnold Math. J. 2 (2016), no. 4, 579-592.

27

Hankel determinants of zeta values (with W. Zudilin), Symmetry, Integrability and Geometry: Methods and Applications 11 (2015), Paper 101.

26

Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices (with H. Koivusalo), Israel J. Math. 212 (2016), no. 1, 189-201.

25

Equivalence classes of codimension one cut-and-project nets, Ergodic Theory Dynam. Systems 36 (2016), no. 3, 816-831.

24

Projective metric number theory (with A. Ghosh), J. Reine Angew. Math. 712 (2016), 39-50.

23

Diophantine approximation and coloring (with S. Munday), Amer. Math. Monthly 122 (2015), no. 6, 567-580.

22

Equivalence relations on separated nets arising from linear toral flows (with M. Kelly, B. Weiss), Proc. Lond. Math. Soc. (3) 109 (2014), no. 5, 1203-1228.

21

Deformation quantization and irrational numbers (with E. Hawkins), J. Symplectic Geom. 12 (2014), no. 1, 1-22.

20

Quantitative ergodic theorems for weakly integrable functions, Ergodic Theory Dyn. Syst. 34 (2014), no. 2, 534-542.

19

Group automorphisms with prescribed growth of periodic points, and small primes in arithmetic progressions in intervals (with C. White), Adv. Math. 252C (2014), 572-585.

18

Metrical musings on Littlewood and friends (with J. L. Jensen, S. Kristensen), Proc. Amer. Math. Soc. 142 (2014), no. 2, 457-466.

17

Density of orbits of semigroups of endomorphisms acting on the Adeles (with S. Munday), New York J. Math. 19 (2013), 443-454.

16

The mixed Littlewood conjecture for pseudo-absolute values (with S. Harrap), Math. Ann. 357 (2013), no.3, 942-960.

15

The Duffin-Schaeffer Conjecture with extra divergence II (with V. Beresnevich, G. Harman, S. Velani), Math Z. 275 (2013), no.1-2, 127-133.

14

Multiplicative zero-one laws and metric number theory (with V. Beresnevich, S. Velani), Acta. Arith. 160 (2013), no.2, 101-114.

13

Incomplete Kloosterman sums and multiplicative inverses in short intervals (with T. D. Browning), Int. J. Number Theory 9 (2013), no.2, 481-486.

12

The Duffin-Schaeffer Conjecture with extra divergence (with A. Pollington, S. Velani), Math. Ann. 353 (2012), no.2, 259-273.

11

Inhomogeneous approximation by coprime integers, New York J. Math. 18 (2012) 249-259.

10

Metric considerations concerning the mixed Littlewood Conjecture (with Y. Bugeaud, S. Velani), Int. J. Number Theory 7 (2011), no. 3, 593-609.

9

A note on Farey fractions with denominators in arithmetic progressions (with D. Badziahin), Acta. Arith. 147 (2011), no.3, 205-215.

8

Numerators of differences of nonconsecutive Farey fractions, Int. J. Number Theory 6 (2010), no.3, 1-12.

7

The metric theory of p-adic approximation, Int. Math. Res. Not. (2010), no.1, 18-52.

6

Intermediate convergents and a metric theorem of Khinchin, Bull. Lond. Math. Soc. 41 (2009), 396-410.

5

The group ring of Q/Z and an application of a divisor problem (with K. Homma), Proc. Amer. Math. Soc. 137 (2009), 1285-1293.

4

Martingale differences and the metric theory of continued fractions (with J. Vaaler), Illinois J. Math. 52 (2008), no.1, 213-242.

3

Tools and techniques in Diophantine approximation, thesis, University of Texas at Austin (2006), 154pp.

2

The distribution of special subsets of the Farey sequence, J. Number Theory 107 (2004), no.1, 95-104.

1

A note on Farey fractions with odd denominators, J. Number Theory 98 (2003), no.1, 89-104.

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