In this section you will find details of my papers, organised by year. You will also find links to preprints of my papers at that awaiting publication, as well as a list of papers that are currently in preparation. There is also a tab for a link to other miscellaneous writings.
A link to my Google Scholar profile can be found here.
I was awarded the Anand Ramachandran Prize for Best PhD Thesis of 2024/25. This prize was endowed in 2015 to commemorate former York PhD graduate Dr Anand Ramachandran by “recognising the love and passion for mathematics”. It is awarded annually for the best PhD thesis during the previous year. The announcement made for this prize is as follows:
Anand Ramachandran Memorial Prize for Best PhD Thesis 2024/25
Congratulations to Dr. Andrew Pearce-Crump, who has been awarded the Anand Ramachandran Memorial Prize for Best PhD Thesis of the last academic year.
Andrew's thesis "Discrete Moments of the Riemann Zeta Function" was supervised by Chris Hughes. The thesis resulted in four published papers (two of which are sole-authored) plus two further papers which are still undergoing peer review, and was also featured in LMS Newsletter as part of their “micro-thesis” series. One of the referees said that the last time a PhD thesis made so many contributions to this field was as long ago as 2007. Both referees spoke positively of how Andrew proactively seeks out collaborations, both during his time as a PhD student and afterwards too. One of the nominators recognised that “the love and passion for mathematics” (as per the prize description) goes beyond just creating new mathematics, it should also include communicating that love and passion through engaging teaching, and that was something Andrew did in abundance during his time in York. Andrew is currently a Heilbronn Fellow at the University of Bristol.
The second moment of the Riemann zeta function at its local extrema
Joint with C. Hughes and S. Lugmayer
Cite as:
Christopher Huges, Solomon Lugmaryer, and Andrew Pearce-Crump, The Second moment of the Riemann zeta function at its local extrema , Journal of the London Mathematical Society, Volume 112, 2025, Pages.
Moments of the Riemann zeta function at its local extrema
Cite as:
Andrew Pearce-Crump, Moments of the Riemann zeta function at its local extrema , Mathematika, Volume 71, 2025, Pages.
A further generalisation of sums of higher derivatives of the Riemann Zeta Function
Cite as:
Andrew Pearce-Crump, A further generalisation of sums of higher derivatives of the Riemann Zeta Function , International Journal of Number Theory, Volume 21, 2025, Pages 357--375.
A heuristic for discrete mean values of the derivative of the Riemann zeta function
Joint with C. Hughes and G. Martin
Cite as:
Christopher Hughes, Greg Martin, Andrew Pearce-Crump, A heuristic for discrete mean values of the derivative of the Riemann zeta function, Integers, Volume 24, 2024, Pages A83.
A discrete mean-value theorem for the higher derivatives of the Riemann zeta function
Joint with C. Hughes
Cite as:
Christopher Hughes, Andrew Pearce-Crump, A discrete mean-value theorem for the higher derivatives of the Riemann zeta function, Journal of Number Theory, Volume 241, 2022, Pages 142--164.
Complex moments of derivative of the Riemann zeta function
Joint with C. Hughes
Integer moments of derivatives of the Riemann zeta function
Joint with C. Hughes
The discrete second moment of mixed derivatives of the Riemann zeta function
Joint with B. Durkan and C. Hughes
Generalisations of the Landau-Gonek Theorem and Applications to Mean Values of Zeta
Joint with B. Durkan and C. Hughes
Generalisations of the Landau-Gonek Theorem and Applications to Mean Values of Zeta
Joint with B. Durkan and C. Hughes