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Kyle Pratt

Contact Information

Office Address:
169 Altgeld Hall
E-mail: kpratt4 (at) illinois (dot) edu

Mailing Address:
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street (MC-382)
Urbana, IL 61801

About Me

I am a fifth-year graduate student working with Kevin Ford. I am interested in number theory, especially prime numbers, sieve methods, exponential sums, and L-functions. Starting in Fall 2019 I will be a Post-Doctoral Research Fellow of All Souls College, University of Oxford.

Publications and Preprints

12. Dirichlet L-functions of quadratic characters of prime conductor at the central point
with Siegfred Baluyot, submitted for publication. arXiv
 
11. Breaking the 1/2-barrier for the twisted second moment of Dirichlet L-functions
with H. M. Bui, N. Robles, A. Zaharescu, submitted for publication. arXiv
 
10. Primes from sums of two squares and missing digits, submitted for publication. arXiv
 
9. Combinatorial applications of autocorrelation ratios
with N. Robles, A. Zaharescu, D. Zeindler, submitted for publication. arXiv
 
8. Average non-vanishing of Dirichlet L-functions at the central point
Algebra Number Theory, Vol. 13 (2019), No. 1, 227–249. arXiv
 
7. Perturbed moments and a longer mollifier for critical zeros of zeta
with N. Robles, Res. Number Theory (2018) 4: 9. arXiv
 
6. A lower bound for the least prime in an arithmetic progression
with J. Li and G. Shakan, Q. J. Math. 68 (2017), no. 3, 729-758. arXiv
 
5. A generalization of the Schur-Siegel-Smyth trace problem
with G. Shakan and A. Zaharescu, J. Math. Anal. Appl. 436 (2016), no. 1, 489-500. arXiv
 
4. Coefficient bounds for level 2 cusp forms
with P. Jenkins, Acta Arithmetica 168 (2015), no. 4, 341-367. arXiv
 
3. Zeros of Dirichlet L-functions over function fields
with J. Andrade, S. J. Miller, and M. Trinh, Communications in Number Theory and Physics 8 (2014), no. 3, 511-539. arXiv
 
2. Special sets of primes in function fields
with J. Andrade, S. J. Miller, and M. Trinh, INTEGERS 14 (2014), #A18. arXiv
 
1. Interlacing of zeros of weakly holomorphic modular forms
with P. Jenkins, Proceedings of the American Mathematical Society, Series B 1 (2014), 63-77. arXiv
 
There may be differences between the arXiv version and the published version of a paper.

Teaching

Fall 2017: I was a TA for sections ADC and ADJ of Math 220.

Spring 2017: I was a TA for sections DDC and DDD of Math 231.

Fall 2016: I was a TA for sections ADJ and ADK of Math 220.

GSNT seminar

In Fall 2018 I am organizing the graduate student number theory seminar. You can find a link to the seminar calendar here.

Curriculum Vitae

CV (updated Sep 24, 2018)

Expository Notes

What is math research?

How to succeed in your UIUC math class