Research

Research Interests

Number theory and arithmetic geometry. I'm interested in elliptic curves and Drinfeld modules, and I work in transcendental number theory related to special values of analytic functions. In particular I work on special values of L-series, modular forms, and hypergeometric functions, and their connections with periods and logarithms.

Texas A&M Number Theory Seminar

Thursdays, 2:30-3:30, Blocker 302

Selected Publications and Preprints

(Click here for Complete List of Publications)

• Hecke L-series for Sinha modules (with E. Davis)
  submitted for publication, 63 pages. [ PDF | arXiv ]

• Convolutions of Goss and Pellarin L-series (with W.-C. Huang)
  submitted for publication, 62 pages. [ PDF | arXiv ]

• A note on log-algebraicity on elliptic curves (with W.-C. Huang)
  submitted for publication, 12 pages. [ PDF | arXiv ]

• Function field analogue of Shimura's conjecture on period symbols
  (with W. D. Brownawell, C.-Y. Chang, and F.-T. Wei)
  submitted for publication, 68 pages. [ PDF | arXiv ]

• Equidistribution of Gross points over rational function fields (with A. El-Guindy, R. Masri, and G. Zeng)
  submitted for publication, 20 pages. [ PDF | arXiv ]

• Hyperderivatives of periods and quasi-periods for Anderson t-modules (with C. Namoijam)
  Memoirs of the American Mathematical Society 302 (2024), no. 1517, v+121 pp. [ Journal | arXiv ]

• Effective rigid analytic trivializations for Drinfeld modules (with C. Khaochim)
  Canadian Journal of Mathematics 75 (2023), no. 3, 713-742. [ Journal | arXiv ]

• Hyperderivative power sums, Vandermonde matrices, and Carlitz multiplication coefficients
  Journal of Number Theory 232 (2022), 317-354. [ Journal | arXiv ]

• A rapid introduction to Drinfeld modules, t-modules, and t-motives (with W. D. Brownawell)
  t-Motives: Hodge Structures, Transcendence, and Other Motivic Aspects,
  European Mathematical Society, Zürich, 2020, pp. 3-30. [ Volume | arXiv ]

• An effective criterion for Eulerian multizeta values in positive characteristic (with C.-Y. Chang and J. Yu)
  Journal of the European Mathematical Society 21 (2019), no. 2, 405-440. [ Journal | arXiv ]

• The de Rham isomorphism for Drinfeld modules over Tate algebras (with O. Gezmiş)
  Journal of Algebra 525 (2019), 454-496. [ Journal | arXiv ]

• Special L-values and shtuka functions for Drinfeld modules on elliptic curves (with N. Green)
  Research in the Mathematical Sciences 5 (2018), 5:4, 47 pp. [ Journal | arXiv ]

• A finite field hypergeometric function associated to eigenvalues of a Siegel eigenform (with D. McCarthy)
  International Journal of Number Theory 11 (2015), no. 8, 2431-2450. [ Journal | arXiv ]

• Identities for Anderson generating functions for Drinfeld modules (with A. El-Guindy)
  Monatshefte für Mathematik 173 (2014), no. 4, 471-493. [ Journal | arXiv ]

• Algebraic independence of periods and logarithms of Drinfeld modules
  (with C.-Y. Chang and with an appendix by B. Conrad)
  Journal of the American Mathematical Society 25 (2012), no. 1, 123-150. [ Journal | arXiv ]

• Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms
  Inventiones Mathematicae 171 (2008), no. 1, 123-174. [ Journal | arXiv ]

• Determination of the algebraic relations among special Γ-values in positive characteristic
  (with G. W. Anderson and W. D. Brownawell)
  Annals of Mathematics 160 (2004), no. 1, 237-313. [ Journal | arXiv ]

• Gaussian hypergeometric functions and traces of Hecke operators (with S. Frechette and K. Ono)
  International Mathematics Research Notices (2004), no. 60, 3233-3262. [ Journal | PDF ]

• Linear independence of Gamma values in positive characteristic (with W. D. Brownawell)
  Journal für die reine und angewandte Mathematik 549 (2002), 91-148. [ Journal | arXiv ]

Graduate Students

• Athena Bassil, Ph.D. student, Texas A&M University

• Jing Ye, Ph.D. student, Texas A&M University

• Erik Davis, Ph.D. 2025, Texas A&M University
  "Goss L-functions of Sinha modules"

• Wei-Cheng Huang, Ph.D. 2023, Texas A&M University
  "Convolutions of Goss L-series and tensor products of Drinfeld modules"

• Chalinee Khaochim, Ph.D. 2021, Texas A&M University
  "Rigid analytic trivializations and periods of Drinfeld modules and their tensor products" [ TAMU Library ]

• Changningphaabi Namoijam, Ph.D. 2020, Texas A&M University
  "Hyperderivatives of periods and logarithms of Anderson t-modules, and algebraic independence" [ TAMU Library ]

• Oğuz Gezmiş, Ph.D. 2019, Texas A&M University
  "Special values of L-series over Tate algebras" [ TAMU Library ]

• Nathan Green, Ph.D. 2018, Texas A&M University
  "Tensor powers of Drinfeld modules and zeta values" [ TAMU Library ]

• Guchao Zeng, Ph.D. 2017, Texas A&M University
  "Theta operators on v-adic modular forms and v-adic families of Goss polynomials and Eisenstein series" [ TAMU Library ]

• Detchat Samart, Ph.D. 2014, Texas A&M University
  "Mahler measures of hypergeometric families of Calabi-Yau varieties" [ TAMU Library ]

• Brad Lutes, Ph.D. 2010, Texas A&M University
  "Special values of the Goss L-function and special polynomials" [ TAMU Library ]

• Valentina Vega, Ph.D. 2009, Texas A&M University
  "Hypergeometric functions over finite fields and their relations to algebraic curves" [ TAMU Library ]

• Jenny Fuselier, Ph.D. 2007, Texas A&M University
  "Hypergeometric functions over finite fields and relations to modular forms and elliptic curves" [ TAMU Library ]