I am a Lecturer in Pure Mathematics at the
University of Manchester. Before moving to Manchester in November 2015, I was a Research Associate at the
University of Bristol
(September 2013 - June 2015), a Postdoc Researcher at
Universität Zürich (September 2011 - August 2013), an EPSRC Postdoctoral Fellow at the
University of Oxford (October 2008 - August 2011), and a Visiting Researcher at the
University of Rochester
(March 2008 - August 2008). I completed my PhD at the University of Bristol in March 2008 under the supervision of Prof.
Jon Keating FRS.
My Erdös number, and also Erdös number of the second kind are 2 (via
Richard Hall).
Research interests
Analytic number theory: analytic theory of the Riemann zeta-function and L-functions, distribution of primes; Sieve methods; Number theory in function fields; Random matrix theory...
Published/Accepted Papers
My profile on MathSciNet, ZentralblattMATH, arXiv and Google Scholar.
(with N.
Evans, S. J.
Lester and K.
Pratt)
Weighted central limit theorems for central values of L-functions, J. Eur. Math. Soc. (JEMS) 27 (2025), 2477-2529 [
journal]
(with A.
Florea and M. B.
Milinovich)
Negative discrete moments of the derivative of the Riemann zeta-function, Bull. London Math. Soc. 56 (2024), 2680-2703 [
journal]
(with K.
Pratt and A.
Zaharescu)
A problem of Erdös-Graham-Granville-Selfridge on integral points on hyperelliptic curves, Math. Proc. Camb. Philos. Soc. 176 (2024) 309-323 [
journal] (see also Terence Tao's
post)
(with A.
Florea)
Negative moments of the Riemann zeta-function, J. Reine Angew. Math. (Crelle's Journal) 806 (2024), 247-288 [
journal]
(with K.
Pratt and A.
Zaharescu)
Analytic ranks of automorphic L-functions and Landau-Siegel zeros, J. London Math. Soc. 109 (2024), e12834 [
journal]
(with D. A.
Goldston, M. B.
Milinovich and H. L.
Montgomery)
Small gaps and small spacings between zeta zeros, Acta Arith. 210 (2023), 133-153 (special issue dedicated to
Andrzej Schinzel). [
journal]
(with R. R.
Hall)
On the derivatives of Hardy's function Z(t), Bull. London Math. Soc. 55 (2023), 2304-2323 [
journal]
(with R. R.
Hall)
A note on the zeros of the derivatives of Hardy's function Z(t), Mathematika 69 (2023), 780-794 [
journal]
(with K.
Pratt and A.
Zaharescu)
Power savings for counting solutions to polynomial-factorial equations, Adv. Math. 422 (2023), 109021 [
journal]
(with A.
Florea and J. P.
Keating)
The Ratios Conjecture and upper bounds for negative moments of L-functions over function fields, Trans. Amer. Math. Soc. 376 (2023), 445-4510 [
journal]
(with K.
Pratt and A.
Zaharescu)
Exceptional characters and nonvanishing of Dirichlet L-functions, Math. Ann. 380 (2021), 593-642 [
journal]
(with A.
Florea and J. P.
Keating)
Type-I contributions to the one and two level densities of quadratic Dirichlet L-functions over function fields, J. Number Theory 221 (2021), 389-423 [
journal]
(with S.
Bettin, X.
Li and M.
Radziwill)
A quadratic divisor problem and moments of the Riemann zeta-function, J. Eur. Math. Soc. (JEMS) 22 (2020), 3953-3980 [
journal]
(with A.
Florea, J. P.
Keating and E.
Roditty-Gershon)
Moments of quadratic twists of elliptic curve L-functions over function fields, Algebra Number Theory 14 (2020), 1853-1893 [
journal]
(with K.
Pratt, N.
Robles and A.
Zaharescu)
Breaking the 1/2 barrier for the twisted second moment of Dirichlet L-functions, Adv. Math. 370 (2020), 107175 [
journal]
(with A.
Florea)
Moments of Dirichlet L-functions with prime conductors over function fields, Finite Fields Appl. 64 (2020), 101659 [
journal]
(with A.
Florea)
Zeros of quadratic Dirichlet L-functions in the hyperelliptic ensemble, Trans. Amer. Math. Soc. 370 (2018), 8013-8045
[
journal]
(with M. B.
Milinovich)
Gaps between zeros of the Riemann zeta-function, Q. J. Math. 69 (2018), 403-423 [
journal]
(with A.
Florea)
Hybrid Euler-Hadamard product for quadratic Dirichlet L-functions in function fields, Proc. London Math. Soc.
117 (2018), 65-99 [
journal]
(with W. P.
Heap and C. L.
Turnage-Butterbaugh)
Gaps between zeros of Dedekind zeta-functions of quadratic number fields. II, Q. J. Math. 67 (2016), 467-482 [
journal]
(with J. P.
Keating and D. J. Smith)
On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class,
J. London Math. Soc. 94 (2016), 161-185 [
journal]
(with S. M.
Gonek and M. B.
Milinovich)
A hybrid Euler-Hadamard product and moments of ζ'(ρ), Forum Math. 27 (2015), 1799-1828 [
journal]
Large gaps between consecutive zeros of the Riemann zeta-function. II, Acta Arith. 165 (2014), 101-122 [
journal]
(with S. J.
Lester and M. B.
Milinovich)
On Balazard, Saias, and Yor's equivalence to the Riemann Hypothesis, J. Math. Anal. Appl. 409 (2014), 244-253 [
journal]
(with D. R.
Heath-Brown)
On simple zeros of the Riemann zeta-function,
Bull. London Math. Soc. 45 (2013), 953-961 [
journal]
Twists of automorphic L-functions at the central point, Int. J. Number Theory 9 (2013), 1015-1053 [
journal]
Non-vanishing of Dirichlet L-functions at the central point, Int. J. Number Theory 8 (2012), 1855-1881 [
journal]
(with M. B.
Milinovich)
Central values of derivatives of Dirichlet L-functions, Int. J. Number Theory
7 (2011), 371-388 [
journal]
Large gaps between consecutive zeros of the Riemann zeta-function, J. Number Theory 131 (2011), 67-95 [
journal]
(with J. B.
Conrey and M. P.
Young)
More than 41% of the zeros of the zeta function are on the critical line,
Acta Arith. 150 (2011), 35-64 [
journal]
(with M. B.
Milinovich and N. C.
Ng)
A note on the gaps between consecutive zeros of the Riemann zeta-function, Proc. Amer. Math. Soc. 138 (2010), 4167-4175 [
journal]
(with D. R.
Heath-Brown)
A note on the fourth moment of Dirichlet L-functions,
Acta Arith. 141 (2010), 335-344 [
journal]
Gaps between zeros of the derivative of the Riemann ξ-function, J. Théor. Nombres Bordeaux 22 (2010), 287-305 [
journal]
A note on the second moment of automorphic L-functions, Mathematika 56 (2010), 35-44 [
journal]
(with J. P.
Keating)
On the mean values of L-functions in orthogonal and symplectic families,
Proc. London Math. Soc. 96 (2008), 335-366 [
journal]
(with J. P.
Keating)
On the mean values of Dirichlet L-functions,
Proc. London Math. Soc. 95 (2007), 273-298 [
journal]
(with J. P.
Keating)
On twin primes associated with the Hawkins random sieve,
J. Number Theory 119 (2006), 284-296 [
journal]
Preprints
(with A.
Florea and H. T.
Ngo)
Simultaneous nonvanishing of Dirichlet L-functions in Galois orbits (Jul 2025) [
arXiv]
(with M. B.
Milinovich and A.
Zaharescu)
A note on the Laguerre and Laguerre-Pólya inequalities for the Riemann Xi-function (Oct 2024)
Critical zeros of the Riemann zeta-function (Oct 2014) [
arXiv]
Others
(with
Lan Hoang),
Lily Bui (2015),
Anne Bui (2018) +
Chau Bui (2025)
(with The-Long Phan, S. C. Yu, R. Vincent, T. D. Thanh, V. D. Lam and Y. P. Lee),
Influence of Mn doping on structural, optical, and magnetic properties of Zn_{1-x}Mn_{x}O nanorods,
J. Appl. Phys. 108 (2010), 044910 [
journal]
Mean values of L-functions, PhD thesis, University of Bristol (2008) (essentially consisted of papers #2, #3 and #4 in the Publications)
Teaching
2024 - 2025: Linear Algebra
2023 - 2024: Number Theory
2022 - 2023: Fourier Analysis and Lebesgue Integration
Number Theory
2021 - 2022: Real Analysis B
Number Theory
2020 - 2021: Real Analysis B
Number Theory
2019 - 2020: Real Analysis B
Number Theory
The Class Number Problem (graduate seminars)
2018 - 2019: Real Analysis B
2017 - 2018: Fourier Analysis and Lebesgue Integration
2016 - 2017: Fourier Analysis and Lebesgue Integration
2015 - 2016: Introduction to Sieve Methods (graduate course), University of Manchester
2011 - 2012: Analytic Number Theory, Universität Zürich
2009 - 2010: Analytic Number Theory, University of Oxford
Links
Miscellany
My
academic genealogy. See also the
family tree (thanks to Ben Odgers), and the
family photo (Jul 2023)
Some conference/workshop photos:
Cambridge 2004,
Rochester 2006,
Trieste 2007,
Banff 2007,
Helsinki 2011,
Bristol 2012,
IAS 2022,
Bristol 2023,
Edinburgh 2023,
Hanoi 2024,
Bristol 2025,
Bonn 2025
A
letter from Trinity College, Cambridge (May 2004)
Among various other things, I collect
stamps about mathematics,
banknotes
featuring mathematicians and physicists (last updated Apr 2010), and
airplane models
A mathematician's apology (G. H.
Hardy, Cambridge University Press 1940, electronic version by Uni. of Alberta Math. Sci. Soc.)
-