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. Sequences, modular forms and cellular integrals (with R. Osburn and A. Straub)
    Submitted for publication, 26 pages.

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

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

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

  5. 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.

  6. 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.

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

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

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

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

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

  12. 3F2 Hypergeometric series and periods of elliptic curves
    International Journal of Number Theory 6 (2010), no. 3, 461-470.

  13. 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