Matthew A. Papanikolas

Department of Mathematics
Texas A&M University
College Station, TX 77843-3368

Citizenship: USA
Place of birth: Tucson, Arizona



Research Interests

Grants Awarded

Publications and Preprints

[1]   Log-algebraicity on tensor powers of the Carlitz module and special values of Goss L-functions
in preparation.
[2]   Log-algebraic identities on Drinfeld modules and special L-values (with C.-Y. Chang and A. El-Guindy)
submitted for publication, 20 pages.
[3]   Special L-values and shtuka functions for Drinfeld modules on elliptic curves (with N. Green)
submitted for publication, 45 pages.
[4]   Theta operators, Goss polynomials, and v-adic modular forms (with G. Zeng)
Journal de Théorie des Nombres de Bordeaux, accepted for publication, 20 pages.
[5]   An effective criterion for Eulerian multizeta values in positive characteristic (with C.-Y. Chang and J. Yu)
Journal of the European Mathematical Society, accepted for publication, 31 pages.
[6]   A rapid introduction to Drinfeld modules, t-modules, and t-motives (with W. D. Brownawell)
t-Motives: Hodge Structures, Transcendence, and Other Motivic Aspects (Banff, AB, 2009), to appear, 24 pages.
[7]   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.
[8]   Identities for Anderson generating functions for Drinfeld modules (with A. El-Guindy)
Monatshefte für Mathematik 173 (2014), no. 4, 471-493.
[9]   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.
[10]   Explicit formulas for Drinfeld modules and their periods (with A. El-Guindy)
Journal of Number Theory 133 (2013), no. 6, 1864-1886.
[11]   Algebraic independence of values of Goss L-functions at s=1 (with B. A. Lutes)
Journal of Number Theory 133 (2013), no. 3, 1000-1011.
[12]   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.
[13]   Algebraic relations among periods and logarithms of rank 2 Drinfeld modules (with C.-Y. Chang)
American Journal of Mathematics 133 (2011), no. 2, 359-391.
[14]   Frobenius difference equations and algebraic independence of zeta values in positive equal characteristic
(with C.-Y. Chang and J. Yu)
Algebra & Number Theory 5 (2011), no. 1, 111-129.
[15]   Algebraic independence of arithmetic gamma values and Carlitz zeta values (with C.-Y. Chang, D. Thakur, and J. Yu)
Advances in Mathematics 223 (2010), no. 4, 1137-1154.
[16]   Geometric Gamma values and zeta values in positive characteristic (with C.-Y. Chang and J. Yu)
International Mathematics Research Notices 2010 (2010), no. 8, 1432-1455.
[17]   Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms
Inventiones Mathematicae 171 (2008), no. 1, 123-174.
[18]   On the torsion of Jacobians of principal modular curves of level 3^n (with C. Rasmussen)
Archiv der Mathematik (Basel) 88 (2007), no. 1, 19-28.
[19]   A formula and a congruence for Ramanujan's tau-function
Proceedings of the American Mathematical Society, 134 (2006), no. 2, 333-341.
[20]   Extensions of abelian varieties defined over a number field (with N. Ramachandran)
Journal of Number Theory 112 (2005), no. 2, 386-400.
[21]   Determination of the algebraic relations among special Gamma-values in positive characteristic
(with G. W. Anderson and W. D. Brownawell)
Annals of Mathematics 160 (2004), no. 1, 237-313.
[22]   Combinatorics of traces of Hecke operators (with S. Frechette and K. Ono)
Proceedings of the National Academy of Sciences, USA, 101 (2004), no. 49, 17016-17020.
[23]   Gaussian hypergeometric functions and traces of Hecke operators (with S. Frechette and K. Ono)
International Mathematics Research Notices, 2004, no. 60, 3233-3262.
[24]   p-adic properties of values of the modular j-function (with K. Ono)
Galois Theory and Modular Forms, Dev. Math., 11, Kluwer, 2004, pp. 357-366.
[25]   Higher Weierstrass points on X_0(p) (with S. Ahlgren)
Transactions of the American Mathematical Society 355 (2003), no. 4, 1521-1535.
[26]   A Weil-Barsotti formula for Drinfeld modules (with N. Ramachandran)
Journal of Number Theory 98 (2003), no. 2, 407-431.
[27]   Universal norms on abelian varieties over global function fields
Journal of Number Theory 94 (2002), no. 2, 326-342.
[28]   Linear independence of Gamma values in positive characteristic (with W. D. Brownawell)
Journal für die reine und angewandte Mathematik 549 (2002), 91-148.
[29]   Quadratic twists of modular forms and elliptic curves (with K. Ono)
Number Theory for the Millennium III (Urbana, IL, 2000), A. K. Peters, 2002, pp. 73-85
[30]   Canonical heights on elliptic curves in characteristic p
Compositio Mathematica 122 (2000), no. 3, 299-313.

Ph.D. Students Supervised

Teaching Experience

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Last modified on August 25, 2017