Matt Papanikolas Professor Department of Mathematics Texas A&M University College Station, TX 77843-3368 Office:   Blocker 332A Blocker 641H Phone: Dept: Fax: (979) 458-1124 (979) 845-7554 (979) 845-6028 Email:   papanikolas@tamu.edu map@math.tamu.edu

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 Group

Texas A&M Number Theory Seminar

Wednesdays, 1:45-2:45, Blocker 220

Southwest Center for Arithmetic Geometry

I am on the advisory board for the Arizona Winter School, held annually in March. Please send your students!

Proceedings of the American Mathematical Society

I am Managing Editor for Proceedings of the AMS.

Education

Ph.D. in Mathematics, Brown University, 1998.
A.B. in Mathematics, Amherst College, 1992.

Curriculum Vitae

• My current CV is available here.

Teaching Information

• Information on courses taught at Texas A&M is available here.

Selected Publications and Preprints

Click here for a Complete List of Publications

• Effective rigid analytic trivializations for Drinfeld modules (with C. Khaochim)
  submitted for publication, 25 pages. [ PDF | arXiv.org ]

• Hyperderivatives of periods and quasi-periods for Anderson t-modules (with C. Namoijam)
  submitted for publication, 111 pages. [ PDF | arXiv.org ]

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

• Hyperderivative power sums, Vandermonde matrices, and Carlitz multiplication coefficients
  Journal of Number Theory, accepted for publication, 32 pages. [ PDF | arXiv.org ]

• t-Motives: Hodge Structures, Transcendence and Other Motivic Aspects (ed. with G. Böckle, D. Goss, and U. Hartl)
  European Mathematical Society, EMS Series of Congress Reports, Vol. 16, Zürich, 2020, 473 pp. [ Volume ]

• 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.org ]

• 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.org ]

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

• Log-algebraic identities on Drinfeld modules and special L-values (with C.-Y. Chang and A. El-Guindy)
  Journal of the London Mathematical Society 97 (2018), no. 2, 125-144. [ Journal | arXiv.org ]

• 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.org ]

• Theta operators, Goss polynomials, and v-adic modular forms (with G. Zeng)
  Journal de Théorie des Nombres de Bordeaux 29 (2017), no. 3, 729-753. [ Journal | arXiv.org ]

• 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.org ]

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

• The Mahler measure of a Calabi-Yau threefold and special L-values (with M. D. Rogers and D. Samart)
  Mathematische Zeitschrift 276 (2014), no. 3-4, 1151-1163. [ Journal | arXiv.org ]

Graduate Students

• Erik Davis, Ph.D. student, Texas A&M University
• Wei-Cheng Huang, Ph.D. student, Texas A&M University
• Chalinee Khaochim, Ph.D. expected 2021, Texas A&M University
  "Rigid analytic trivializations and periods of Drinfeld modules and their tensor products"
• Changningphaabi Namoijam, Ph.D. 2020, Texas A&M University
  "Hyperderivatives of periods and logarithms of Anderson t-modules, and algebraic independence"
• 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 | PDF ]
• 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 ]