- Transitive subtournaments of
*k*-th power Paley digraphs and improved lower bounds for Ramsey numbers

(with M. Springfield)

Submitted.

[ Journal | arXiv | Download Python Code ]

- The number of 𝔽
_{q}-points on diagonal hypersurfaces with monomial deformation

Submitted.

[ Journal | arXiv ]

- Orbits of Finite Field Hypergeometric Functions and Complete Subgraphs of Generalized Paley Graphs

(with M. Springfield)

Involve, accepted for publication.

[ Journal | arXiv | Download Python Code ]

- Eigenvalues and Fourier coefficients of degree two Siegel eigenforms constructed from Igusa theta constants

Research in Number Theory, 8:88 (2022).

[ Journal | Journal (free view) | arXiv ]

- Hypergeometric Functions over Finite Fields and Modular Forms: A Survey and New Conjectures

(with M. Locus Dawsey)

Operator Theory: Advances and Applications 285, (2021) 41-56.

[ Journal | arXiv ]

- Generalized Paley Graphs and their Complete Subgraphs of Orders Three and Four

(with M. Locus Dawsey)

Research in the Mathematical Sciences, 8:18 (2021) .

[ Journal | arXiv ]

- Sequences, modular forms and cellular integrals

(with R. Osburn and A. Straub)

Mathematical Proceedings of the Cambridge Philosophical Society, 168(2) (2020), 379-404.

[ Journal | arXiv ]

- On a question of Zhang

(with Y. Yang)

Communications in Algebra, (2019) 47:12, 5133-5134.

[ Journal ]

- Apéry-like numbers and families of newforms with complex
multiplication

(with A. Gomez and D. Young)

Research in Number Theory, 5:5 (2019).

[ Journal | arXiv ]

- The number of 𝔽
_{p}-points on Dwork hypersurfaces and hypergeometric functions

Research in the Mathematical Sciences, 4:4 (2017).

[ Journal | arXiv ]

- Multiplicative relations for Fourier coefficients of degree 2 Siegel eigenforms

Journal of Number Theory, 170 (2017), 263-281.

[ Journal | arXiv ]

- Hypergeometric type identities in the p-adic setting and modular forms

(with J. Fuselier)

Proceedings of the American Mathematical Society, 144 (2016), 1493-1508.

[ Journal | arXiv ]

- 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.

[ Journal | arXiv ]

- 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.

[ Journal | arXiv ]

- The trace of
Frobenius of
elliptic curves and the p-adic gamma
function

Pacific Journal of Mathematics, 261 (2013), no. 1, 219-236.

[ Journal | arXiv ]

- Transformations
of
well-poised hypergeometric functions over finite fields

Finite Fields and Their Applications, 18 (2012), no. 6, 1133-1147.

[ Journal | arXiv ]

- On a
supercongruence
conjecture of Rodriguez-Villegas

Proceedings of the American Mathematical Society, 140 (2012), 2241-2254.

[ Journal | arXiv ]

- Extending
Gaussian
hypergeometric series to the p-adic setting

International Journal of Number Theory, 8 (2012), no. 7, 1581-1612.

[ Journal | arXiv ]

- Binomial
coefficient-harmonic sum identities associated to supercongruences

Integers, 11 (2011), A37, 8 pp.

[ Journal | arXiv ]

_{3}F_{2}Hypergeometric series and periods of elliptic curves

International Journal of Number Theory, 6 (2010), no. 3, 461-470.

[ Journal | arXiv ]

- A p-adic
analogue of a formula of Ramanujan

(with R. Osburn)

Archiv der Mathematik, 91 (2008), no. 6, 492-504.

[ Journal | arXiv ]

- Sequences, modular forms and cellular integrals

(with R. Osburn and A. Straub)

2017 MATRIX Annals, edited by David R. Wood et al., MATRIX Book Series 2, Springer, 2019.

[ Series | Book ]