**Publications**

**Preprints**

**1. Mean Values of Derivatives of $L$-functions in function fields: III**

accept (to appear in Proceedings of the Royal Society of Edinburgh, Section A: Mathematics).

**2. On Elementary Estimates of Arithmetic Sums for Polynomial Rings over Finite Fields**

with C. Summersby and A. Shamesaldeen

accept (to appear in the Journal of Number Theory)

**3. Universality of $L$-functions over Function Fields**

with S. Gonek

submitted.

**4. Mean Values of Derivatives of $L$-functions in function fields: IV**

with H. Jung

submitted.

**5. On the Average Value of Unitary Divisors and Semiprimes in $\mathbb{F}_{q}[t]$**

with J. Cabral

submitted

**6. On a special case of the binary additive divisor problem**

with K. Smith

submitted.

**7. On the Splitting of Integral Moments of $\zeta$ and $\zeta^{'}/\zeta$**

with K. Smith

submitted.

**8. Small Zeros of Dirichlet $L$-functions of Quadratic Characters of Prime Modulus**

with S. Baluyot

submitted.

**9. Integral Moments and Ratios of Quadratic Dirichlet $L$-functions over monic irreducible polynomials in $\mathbb{F}_{q}[T]$**

with H Jung and A. Shamesaldeen

submitted.

**10. The Hybrid Euler-Hadamard formula for**

**Quadratic Dirichlet $L$-functions over monic irreducible polynomials in $\mathbb{F}_{q}[T]$**

with A. Shamesaldeen

submitted.

**11. Generalisations of Ramanujan Sums for Polynomial Rings over Finite Fields**

with J. Hanslope

submitted.

****

**12. Random matrix theory, moments of $\zeta(s)$ and noncommutative geometry**

with A. Connes

in preparation.

**13. A Note on Extreme Values of $L(s,\chi_{D})$ in $\mathbb{F}_{q}(T)$.**

in preparation.

**Publications**

**1. The Mean Value of $L(\tfrac{1}{2}, \chi)$ in the Hyperelliptic Ensemble**

with J. P. Keating

Journal of Number Theory, Volume 132, Issue 12 (2012) pp. 2793-2816.

**2. A Note on the Mean Value of $L$-functions in Function Fields**

International Journal of Number Theory, Vol. 08, No. 07, (2012) pp. 1725-1740.

**3. Mean Value Theorems for $L$-functions over prime polynomials for the rational function field**

with J. P. Keating

Acta Arithmetica, Vol. 161, (2013) pp. 371-385.

**4. Hilbert-Pólya Conjecture, Zeta Functions and Bosonic Quantum Field Theories**

International Journal of Modern Physics A, Vol. 28, (2013) p. 1350072.

**5. The $abc$-conjecture**

Klein Mathematical Project (in portuguese), Vol. 01, (2013) pp. 1-6.

**6. Conjectures for the Integral Moments and Ratios of $L$-functions over function fields**

with J. P. Keating

Journal of Number Theory, Vol. 142, (2014) pp. 102-148.

**7. Newman's Conjecture in various settings**

with S. J. Miller and A. Chang

Journal of Number Theory, Vol. 144 (2014) pp. 70-91.

**8. Special Sets of Primes in Function Fields**

with S. J. Miller, K. Pratt and M. Trinh

Integers, Vol. 14, (2014) pp. 1-4.

**9. Zeros of Dirichlet $L$-functions over function fields**

with S.J. Miller, K. Pratt and M. Trinh

Communications in Number Theory and Physics , Vol. 8, No. 3 (2014), pp. 511-539.

**10. Shifted Convolution and the Titchmarsh divisor problem over $\mathbb{F}_{q}[t]$**

with Z. Rudnick and L. Bary-Soroker

Philosophical Transactions Royal Society A, Vol. 373, (2015), p. 20140308-20140308.

See erratum correcting a misprint here.

**11. A Simple Proof of the Mean Value of $|K_{2}(\mathcal{O})|$ in function fields**

C.R. Acad. Sci. Paris, Vol. 353, (2015), pp. 677-682.

**12. Mean Values of Derivatives of $L$-functions in Function Fields: I**

with S. Rajagopal

Journal of Mathematical Analysis and Applications, Vol. 443, (2016), pp. 526-541.

**13. Average Values of $L$-series for real characters in function fields.**

with S. Bae and H. Jung

Research in the Mathematical Sciences, Vol. 3, (2016), pp. 38.

**14. Rudnick and Soundararajan's theorem for function fields.**

Finite Fields and Their Applications, Vol. 37, (2016), pp. 311-327.

**15. Mean Values of Derivatives of $L$-functions in Function Fields: II**

Journal of Number Theory, Vol.183, (2018), pp. 24 -39.

**16. On the Pairwise of Generalized Divisor Functions**

with K. Smith

Quarterly Journal of Mathematics, Vol. 69, Issue 3, (2018), pp. 943-950.

**17. Mean Value of the class number in function fields revisited**

with H. Jung

Monatshefte fur Mathematik, Volume 187, Issue 4, (2018), 577-602.

**18. Truncated Product Representations for $L$-functions in the Hyperelliptic Ensemble**

with S. Gonek and J. Keating

Mathematika, Vol.64, (2018), pp. 137 - 158.

**Book Chapters, Theses and Other Writings**

****

**Random Matrix Theory and $L$-functions in Function Fields**

PhD Thesis, University of Bristol, 2012

Advisor: J.P. Keating and N.C. Snaith

**Theta Functions: The Problem of the Representation of Numbers as Sums of Square**

Undergraduate Junior Paper, Sao Paulo State University, 2005

Advisor: S. Christodoulou