Contact Information

Dermot McCarthy
Department of Mathematics & Statistics
Texas Tech University
Lubbock, TX 79409-1042

Ph: (806) 834-0191

E-mail: dermot.mccarthy@ttu.edu

Employment

Assistant Professor, Department of Mathematics & Statistics, Texas Tech University, September 2013 - present.

Visiting Assistant Professor, Department of Mathematics, Texas A&M University, September 2010 - August 2013.

Education

Ph.D. Mathematics, University College Dublin, Ireland, June 2010.
Dissertation: p-adic Hypergeometric Series and Supercongruences
Advisor: Dr. Robert Osburn

B.Sc. Mathematics (First Class Honors), Dublin Institute of Technology, Ireland, October 2004.

Research Interests

Number theory, modular forms, hypergeometric functions, properties of algebraic varieties.

Publications

  1. Apéry-like numbers and families of newforms with complex multiplication (with A. Gomez and D. Young)
    Research in Number Theory (2019) 5:5.

  2. Sequences, modular forms and cellular integrals (with R. Osburn and A. Straub)
    Mathematical Proceedings of the Cambridge Philosophical Society, to appear, 26 pages.

  3. The number of $\mathbb{F}_p$-points on Dwork hypersurfaces and hypergeometric functions
    Research in the Mathematical Sciences (2017) 4:4.

  4. Multiplicative relations for Fourier coefficients of degree 2 Siegel eigenforms
    Journal of Number Theory, 170 (2017), 263-281.

  5. Hypergeometric type identities in the p-adic setting and modular forms (with J. Fuselier)
    Proceedings of the American Mathematical Society 144 (2016), 1493-1508.

  6. A finite field hypergeometric function associated to eigenvalues of a Siegel eigenform (with M. Papanikolas)
    International Journal of Number Theory 11 (2015), no. 8, 2431-2450.

  7. Summation identities and special values of hypergeometric series in the p-adic setting (with R. Barman and N. Saikia)
    Journal of Number Theory, 153 (2015), 63-84.

  8. The trace of Frobenius of elliptic curves and the p-adic gamma function
    Pacific Journal of Mathematics, 261 (2013), no. 1, 219-236.

  9. Transformations of well-poised hypergeometric functions over finite fields
    Finite Fields and Their Applications, 18 (2012), no. 6, 1133-1147.

  10. On a supercongruence conjecture of Rodriguez-Villegas
    Proceedings of the American Mathematical Society 140 (2012), 2241-2254.

  11. Extending Gaussian hypergeometric series to the p-adic setting
    International Journal of Number Theory 8 (2012), no. 7, 1581-1612.

  12. Binomial coefficient-harmonic sum identities associated to supercongruences
    Integers 11 (2011), A37, 8 pp.

  13. 3F2 Hypergeometric series and periods of elliptic curves
    International Journal of Number Theory 6 (2010), no. 3, 461-470.

  14. A p-adic analogue of a formula of Ramanujan (with R. Osburn)
    Archiv der Mathematik 91 (2008), no. 6, 492-504.

Invited Talks

Contributed & Other Talks

Service

Awards