Please be aware that the published version may differ slightly from the arXiv version.
Please be aware that the published version may differ slightly from the arXiv version.
20. On the existence of magic squares of powers (with N. Rome).
arXiv:2406.09364. Research in Number Theory, to appear.
19. Integral solutions to systems of diagonal equations (with N. Rome).
arXiv:2406.09256. Pacific Journal of Mathematics, to appear.
18. Rational curves on complete intersections and the circle method (with T.D. Browning and P. Vishe).
17. Quartic polynomials in two variables do not represent all non-negative integers (with S.Y. Xiao).
arXiv:2307.05712. Journal of the European Mathematical Society, to appear.
16. Birch's theorem on forms in many variables with a Hessian condition.
arXiv:2304.02620. Acta Arithmetica, to appear.
15. Diophantine equations in primes: density of prime points on affine hypersurfaces II.
arXiv:2111.06122.
14. Density of rational points near/on compact manifolds with certain curvature conditions (with D.
Schindler).
Adv. Math. 403 (2022), Paper No. 108358, 36 pp.
13. Diophantine equations in primes: density of prime points on affine hypersurfaces.
Duke Math. J. 171 (4) (2022), 831-884.
12. On an oscillatory integral involving a homogeneous form.
Funct. Approx. Comment. Math. 62 (2020), 21-58.
11. Arithmetic of higher-dimensional orbifolds and a mixed Waring problem (with T.D. Browning).
Math. Z. 299 (2021), no. 1-2, 1071-1101.
10. Diophantine equations in semiprimes.
Discrete Analysis 2019:17, 21 pp.
9. Prime solutions to polynomial equations in many variables and differing degrees.
Forum Math. Sigma 6 (2018), e19, 89 pp.
8. An exponential sum estimate for systems including linear polynomials.
J. Théorie Nombres Bordeaux 30 (2018), 485-499.
7. Zeroes of polynomials with prime inputs and Schmidt's $h$-invariant (with S.Y. Xiao).
Canad. J. Math. 72 (2020), no. 3, 805-833.
6. Sidon basis in polynomial rings over finite fields (with W. Kuo).
Czechoslovak Math. J. 71 (146) (2021), no. 2, 555-562.
5. On a problem of Sidon for polynomials over finite fields (with W. Kuo).
Acta Arith. 174 (2016), no. 3, 239-254.
4. The asymptotic formula for Waring's problem in function fields.
Internat. Math. Res. Notices (2016) 2016, no. 23, 7137-7178.
3. Diophantine approximation of polynomials over $\mathbb{F}_q[t]$ satisfying a divisibility condition.
Int. J. Number Theory 12 (2016), no. 5, 1371-1390.
2. A generalization of a theorem of Erdős-Rényi to $m$-fold sums and differences (with K.E. Hare).
Acta Arith. 166 (2014), no. 1, 55-67.
1. Computing the moment polynomials of the zeta function (with M.O. Rubinstein).
Math. Comp. 84 (2015), no. 291, 425-454.