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 is 2.
Research interests
Analytic number theory: analytic theory of the Riemann zetafunction and Lfunctions, 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 R. R.
Hall)
On the derivatives of Hardy's function Z(t), to appear in Bull. London Math. Soc. [
arXiv]
(with R. R.
Hall)
A note on the zeros of the derivatives of Hardy's function Z(t), to appear in Mathematika [
arXiv]
(with D. A.
Goldston, M. B.
Milinovich and H. L.
Montgomery)
Small gaps and small spacings between zeta zeros, to appear in Acta Arith. [
journal]
(with K.
Pratt and A.
Zaharescu)
Power savings for counting solutions to polynomialfactorial equations, Adv. Math. 422 (2023), 109021 [
journal]
(with A.
Florea and J. P.
Keating)
The Ratios Conjecture and upper bounds for negative moments of Lfunctions over function fields, Trans. Amer. Math. Soc. 376 (2023), 44534510 [
journal]
(with K.
Pratt and A.
Zaharescu)
Exceptional characters and nonvanishing of Dirichlet Lfunctions, Math. Ann. 380 (2021), 593642 [
journal]
(with A.
Florea and J. P.
Keating)
TypeI contributions to the one and two level densities of quadratic Dirichlet Lfunctions over function fields, J. Number Theory 221 (2021), 389423 [
journal]
(with S.
Bettin, X.
Li and M.
Radziwill)
A quadratic divisor problem and moments of the Riemann zetafunction, J. Eur. Math. Soc. (JEMS) 22 (2020), 39533980 [
journal]
(with A.
Florea, J. P.
Keating and E.
RodittyGershon)
Moments of quadratic twists of elliptic curve Lfunctions over function fields, Algebra Number Theory 14 (2020), 18531893 [
journal]
(with K.
Pratt, N.
Robles and A.
Zaharescu)
Breaking the 1/2barrier for the twisted second moment of Dirichlet Lfunctions, Adv. Math. 370 (2020), 107175 [
journal]
(with A.
Florea)
Moments of Dirichlet Lfunctions with prime conductors over function fields, Finite Fields Appl. 64 (2020), 101659 [
journal]
(with A.
Florea)
Zeros of quadratic Dirichlet Lfunctions in the hyperelliptic ensemble, Trans. Amer. Math. Soc. 370 (2018), 80138045
[
journal]
(with M. B.
Milinovich)
Gaps between zeros of the Riemann zetafunction, Q. J. Math. 69 (2018), 403423 [
journal]
(with A.
Florea)
Hybrid EulerHadamard product for quadratic Dirichlet Lfunctions in function fields, Proc. London Math. Soc.
117 (2018), 6599 [
journal]
(with W. P.
Heap and C. L.
TurnageButterbaugh)
Gaps between zeros of Dedekind zetafunctions of quadratic number fields. II, Q. J. Math. 67 (2016), 467482 [
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 Lfunctions in the Selberg class,
J. London Math. Soc. 94 (2016), 161185 [
journal]
(with S. M.
Gonek and M. B.
Milinovich)
A hybrid EulerHadamard product and moments of ζ'(ρ), Forum Math. 27 (2015), 17991828 [
journal]
Large gaps between consecutive zeros of the Riemann zetafunction. II, Acta Arith. 165 (2014), 101122 [
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), 244253 [
journal]
(with D. R.
HeathBrown)
On simple zeros of the Riemann zetafunction,
Bull. London Math. Soc. 45 (2013), 953961 [
journal]
Twists of automorphic Lfunctions at the central point, Int. J. Number Theory 9 (2013), 10151053 [
journal]
Nonvanishing of Dirichlet Lfunctions at the central point, Int. J. Number Theory 8 (2012), 18551881 [
journal]
(with M. B.
Milinovich)
Central values of derivatives of Dirichlet Lfunctions, Int. J. Number Theory
7 (2011), 371388 [
journal]
Large gaps between consecutive zeros of the Riemann zetafunction, J. Number Theory 131 (2011), 6795 [
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), 3564 [
journal]
(with M. B.
Milinovich and N. C.
Ng)
A note on the gaps between consecutive zeros of the Riemann zetafunction, Proc. Amer. Math. Soc. 138 (2010), 41674175 [
journal]
(with D. R.
HeathBrown)
A note on the fourth moment of Dirichlet Lfunctions,
Acta Arith. 141 (2010), 335344 [
journal]
Gaps between zeros of the derivative of the Riemann ξfunction, J. Théor. Nombres Bordeaux 22 (2010), 287305 [
journal]
A note on the second moment of automorphic Lfunctions, Mathematika 56 (2010), 3544 [
journal]
(with J. P.
Keating)
On the mean values of Lfunctions in orthogonal and symplectic families,
Proc. London Math. Soc. 96 (2008), 335366 [
journal]
(with J. P.
Keating)
On the mean values of Dirichlet Lfunctions,
Proc. London Math. Soc. 95 (2007), 273298 [
journal]
(with J. P.
Keating)
On twin primes associated with the Hawkins random sieve,
J. Number Theory 119 (2006), 284296 [
journal]
Preprints
(with A.
Florea)
Negative moments of the Riemann zetafunction (Feb 2023) [
arXiv]
(with K.
Pratt and A.
Zaharescu)
A problem of ErdösGrahamGranvilleSelfridge on integral points on hyperelliptic curves (Nov 2022) [
arXiv]
(with N.
Evans, S. J.
Lester and K.
Pratt)
Weighted central limit theorems for central values of Lfunctions (Sep 2021) [
arXiv]
(with K.
Pratt and A.
Zaharescu)
Analytic ranks of automorphic Lfunctions and LandauSiegel zeros (Mar 2021) [
arXiv]
Critical zeros of the Riemann zetafunction (Oct 2014) [
arXiv]
Others
Mean values of Lfunctions, PhD thesis, University of Bristol (2008) (essentially consisted of papers #2, #3 and #4 in the Publications)
Teaching
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
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
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.)
