Publications
Preprints
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.
19. On Elementary Estimates of Arithmetic Sums for Polynomial Rings over Finite Fields
with C. Summersby and A. Shamesaldeen
Journal of Number Theory, Vol.199, (2019), pp. 49 - 62.
20. Mean Values of Derivatives of $L$-functions in function fields: III
Proc. Roy. Soc. Edinburgh Sect. A, 149 (2019), pp. 905 - 913.
21. Small Zeros of Dirichlet $L$-functions of Quadratic Characters of Prime Modulus
with S. Baluyot
Res. Number Theory, Vol.6, 18, (2020)
22. The Fourth Power Mean of Dirichlet $L$-functions in $\mathbb{F}_{q}[T]$.
with M. Yiasemides
Rev Mat Complut, Vol. 34 (2021), pp. 239-296.
23. The First Moment of $L(1/2,\chi)$ for Real Quadratic Function Fields
with J. MacMillan
Acta Arithmetica, Vol. 198 (2021), pp.1-35.
24. The Fourth Moment of Derivatives of Dirichlet $L$-functions in Function Fields
with M. Yiasemides
Mathematische Zeitschrift, Vol. 299 (2021), pp. 671-697.
25. The Integral Moments and Ratios of Quadratic Dirichlet $L$-functions over Monic Irreducible Polynomials in $\mathbb{F}_{q}[T]$.
with H. Jung and A. Shamesaldeen
The Ramanujan Journal, Vol. 56 (2021), pp. 23-66.
26. The Moments and Statistical Distribution of Class Number of Primes over Function Fields.
with A. Shamesaldeen
Finite Fields and Their Applications, Vol. 73 (2021), 101845.
27. Mean Values of Derivatives of $L$-functions in function fields: IV
with H. Jung
J. Korean Math. Soc., Vol. 58, No.6 (2021), 1529-1547
28. Random Matrix Theory and Moments of Moments of L-functions
with C.G. Best
(accept) to appear in Random Matrices: Theory and Applications (2022).
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.
19. On Elementary Estimates of Arithmetic Sums for Polynomial Rings over Finite Fields
with C. Summersby and A. Shamesaldeen
Journal of Number Theory, Vol.199, (2019), pp. 49 - 62.
20. Mean Values of Derivatives of $L$-functions in function fields: III
Proc. Roy. Soc. Edinburgh Sect. A, 149 (2019), pp. 905 - 913.
21. Small Zeros of Dirichlet $L$-functions of Quadratic Characters of Prime Modulus
with S. Baluyot
Res. Number Theory, Vol.6, 18, (2020)
22. The Fourth Power Mean of Dirichlet $L$-functions in $\mathbb{F}_{q}[T]$.
with M. Yiasemides
Rev Mat Complut, Vol. 34 (2021), pp. 239-296.
23. The First Moment of $L(1/2,\chi)$ for Real Quadratic Function Fields
with J. MacMillan
Acta Arithmetica, Vol. 198 (2021), pp.1-35.
24. The Fourth Moment of Derivatives of Dirichlet $L$-functions in Function Fields
with M. Yiasemides
Mathematische Zeitschrift, Vol. 299 (2021), pp. 671-697.
25. The Integral Moments and Ratios of Quadratic Dirichlet $L$-functions over Monic Irreducible Polynomials in $\mathbb{F}_{q}[T]$.
with H. Jung and A. Shamesaldeen
The Ramanujan Journal, Vol. 56 (2021), pp. 23-66.
26. The Moments and Statistical Distribution of Class Number of Primes over Function Fields.
with A. Shamesaldeen
Finite Fields and Their Applications, Vol. 73 (2021), 101845.
27. Mean Values of Derivatives of $L$-functions in function fields: IV
with H. Jung
J. Korean Math. Soc., Vol. 58, No.6 (2021), 1529-1547
28. Random Matrix Theory and Moments of Moments of L-functions
with C.G. Best
(accept) to appear in Random Matrices: Theory and Applications (2022).
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
