# mixedmath

Explorations in math and programming
David Lowry-Duda

I'm a senior research scientist at ICERM and Brown University. I'm supported by the Simon's Collaboration on arithmetic geometry, number theory, and computation. I mostly research analytic number theory, computational number theory and geometry, and arithmetic geometry.

Previously, I was a postdoctoral researcher at the University of Warwick. I received my PhD at Brown University with Jeff Hoffstein as my PhD advisor.

### Publications and Preprints

This is mostly in reverse chronological order. Please note that I upload preprints of all of my papers to the arxiv. If you have trouble accessing one of my papers, email me and I'll send you a copy.

1. Chan Ieong Kuan, David Lowry-Duda, and Alexander Walker. Counting divisors in the outputs of a quadratic polynomial. Preprint soon available.

2. Theresa C. Anderson, Ayla Gafni, Kevin Hughes, Robert J. Lemke Oliver, David Lowry-Duda, Frank Thorne, Jiuya Wang, and Ruixiang Zhang. Improved bounds on number fields of small degree. arxiv preprint
Paper discussion page.
Other pages discussing this work: simplified proofs.
Talks discussing this work: May 2022.

3. Theresa C. Anderson, Ayla Gafni, Robert J. Lemke Oliver, David Lowry-Duda, George Shakan, and Ruixiang Zhang. Quantitative Hilbert irreducibility and almost prime values of polynomial discriminants. To appear in International Mathematics Research Notices. arxiv preprint.
Paper discussion page.

4. David Lowry-Duda. Sign changes of cusp form coefficients on indices that are sums of two squares. arxiv preprint.

5. Anupam Datta, Nir Elber, Raymond Feng, David Lowry-Duda, and Henry Xie. Prime Sums. arxiv preprint.
(This comes from a PROMYS research project for high schoolers).

6. Thomas Hulse, Chan Ieong Kuan, David Lowry-Duda, and Alexander Walker. Arithmetic progressions of squares and multiple Dirichlet series. arxiv preprint.

7. David Lowry-Duda, Takashi Taniguchi, and Frank Thorne. Uniform bounds for lattice point counting and partial sums of zeta functions. To appear in Mathematische Zeitschrift. arxiv preprint.

8. David Lowry-Duda. Visualizing modular forms. To appear in Arithmetic Geometry, Number Theory, and Computation volume in Simons Symposia series. arxiv preprint.

9. David Lowry-Duda, with an appendix by Brendan Hassett. Congruent numbers with the same hypotenuse. To appear in Arithmetic Geometry, Number Theory, and Computation volume in Simons Symposia series. arxiv preprint.

10. Alex J. Best, Jonathan Bober, Andy R. Booker, Edgar Costa, John Cremona, Martin Derickx, David Lowry-Duda, Min Lee, David Roe, Andrew V. Sutherland, and John Voight. Computing classical modular forms. To appear in Arithmetic Geometry, Number Theory, and Computation volume in Simons Symposia. arxiv preprint.

11. Thomas Hulse, Chan Ieong Kuan, David Lowry-Duda, and Alexander Walker. Triple correlation sums of coefficients of cusp forms. Journal of Number Theory 2020 (2021): 1-18. arxiv preprint.

12. Thomas Hulse, Chan Ieong Kuan, David Lowry-Duda, and Alexander Walker. The Laplace transform of the second moment in the Gauss circle problem. Algebra and Number Theory 15 No. 1 (2021): 1-27. arxiv preprint.

13. David Lowry-Duda and Adam Sakareassen. Towards flying through modular forms. Proceedings of Bridges (2021). arxiv preprint.

14. David Lowry-Duda. Non-real poles and irregularity of distribution. Journal of Number Theory, 217 (2020): 23-35. arxiv preprint.

15. David Lowry-Duda and Miles Wheeler. Perturbing the mean value theorem: implicit functions, the Morse lemma, and beyond. The American Mathematical Monthly, 128 No. 1 (2020): 50-61. arxiv preprint.

16. Thomas Hulse, Chan Ieong Kuan, David Lowry-Duda, and Alexander Walker. A shifted problem for the congruent number problem. Ramanujan Journal (2019): 1-8. arxiv preprint.

17. Thomas Hulse, Chan Ieong Kuan, David Lowry-Duda and Alexander Walker. Second moments in the generalized Gauss circle problem. Forum of Mathematics, Sigma, 6 (2018): e24. arxiv preprint.
Paper discussion page.

18. Alina Bucur, Edgar Costa, Chantal David, João Guerreiro, and David Lowry-Duda. Traces, high powers and one level density for families of curves over finite fields. Mathematical Proceedings of the Cambridge Philsophical Society 165 No. 2 (2018): 225-248. arxiv preprint.

19. Thomas Hulse, Chan Ieong Kuan, David Lowry-Duda, and Alexander Walker. Short-Interval Averages of Sums of Fourier Coefficients of Cusp Forms. Journal of Number Theory, 173 (2017): 394-415. arxiv preprint.
Paper discussion page.

20. Thomas Hulse, Chan Ieong Kuan, David Lowry-Duda, and Alexander Walker. Sign-Changes of Sums of Fourier Coefficients of Cusp Forms. Journal of Number Theory, 177 (2017): 112-135. arxiv preprint.
Paper discussion page.

21. Thomas Hulse, Chan Ieong Kuan, David Lowry-Duda, and Alexander Walker. The Second Moment of Sums of Coefficients of Cusp Forms. Journal of Number Theory,  173 (2017): 304-331. arxiv preprint.
Paper discussion page.

22. Paul Carter and David Lowry-Duda. On Functions whose Mean-Value Abscissas are Midpoints. The American Mathematical Monthly, 124 No. 6 (2017): 535-542. arxiv preprint.
Paper discussion page.

23. David Lowry-Duda. On Some Variants of the Gauss Circle Problem. PhD Thesis at Brown University, 2017. arxiv preprint.

24. David Lowry-Duda. Unexpected Conjectures about -5 modulo primes, Classroom Capsule in College Math Journal Vol 46 No. 1, January 2015.

### Unpublished research notes

In addition to the unpublished notes on this site, I've written the following notes and do not intend to publish them.

1. David Lowry-Duda. A Short Note on Gaps between Powers of Consecutive Primes. Unpublished note (2017). arxiv preprint.
Discussion page.

2. David Lowry-Duda. A Friendly Intro to Sieves with a Look Towards Recent Progress on the Twin Primes Conjecture. Unpublished note (2013). arxiv preprint.
Discussion page.