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 A.

Florea)

*Negative moments of the Riemann zeta-function*, to appear in J. Reine Angew. Math. (Crelle's Journal) [

arXiv]

(with N.

Evans, S. J.

Lester and K.

Pratt)

*Weighted central limit theorems for central values of L-functions*, to appear in J. Eur. Math. Soc. (JEMS) [

arXiv]

(with K.

Pratt and A.

Zaharescu)

*Analytic ranks of automorphic L-functions and Landau-Siegel zeros*, to appear in J. London Math. Soc. [

journal]

(with K.

Pratt and A.

Zaharescu)

*A problem of Erdös-Graham-Granville-Selfridge on integral points on hyperelliptic curves*, to appear in Math. Proc. Camb. Philos. Soc. [

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), 4453-4510 [

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 M. B.

Milinovich)

*Negative discrete moments of the derivative of the Riemann zeta-function* (Oct 2023) [

arXiv]

*Critical zeros of the Riemann zeta-function* (Oct 2014) [

arXiv]

Others

*Mean values of L-functions*, 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

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

Manchester Number Theory

seminar (If you happen to be in the UK and would like to give a talk in Manchester, please let me know)

Number Theory Web

seminar

PIMS Collaborative Research Group

seminar

Lecture

videos in Number Theory