## 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

### Expository Notes