Nathan Green
Office: Nethken 221
E-mail: ngreen [AT] latech.edu
I am an assistant professor in mathematics at Louisiana Tech University in Ruston, LA.
Research Interests
My research is in algebraic number theory and focuses on special values of zeta functions, multiple zeta functions and L-functions in function fields. In particular, I apply techniques from Drinfeld modules to study these special values. One of the main goals driving my research is to understand the transcendence of and algebraic relations between these special values.
Funding
My work is currently supported by:
Research Competitiveness Subprogram grant (RCS) funded by the Board of Regents of the state of Louisiana - 06/23 through 06/26 - $148,109
NSF Algebra and Number Theory grant 2302399 - 09/23 through 09/26 - $139,074
Interdisciplinary Art Grant
In 2019-2020 I worked with UCSD MFA student Grace Grothaus to create a visual represenation of my research in transcendental number theory. Here is a small sample of the completed project, called "Transcendere". Our work was funded by a mini-grant from the Research Communications Program of UCSD Physical Sciences.
You can also see a short video clip showing the effect the iridescent inks give the painting. The painting is displayed in the AP&M building at UCSD.
Teaching
2023 - 2024 - See Canvas
Math 416 - Spring 2022 - Course Webpage
Math 470 - Winter 2022 - Course Webpage
Math 408 - Fall 2021 - Course Webpage
Math 20B - Summer 2021 - Course Webpage
Math 103B - Spring 2021 - Course Webpage
Math 20A - Winter 2021 - Course Webpage
Math 103A - Winter 2021 - Course Webpage
Math 20B - Fall 2020 - Course Webpage
Math 103B - Winter 2020 - Course Webpage
Math 102 - Fall 2019 - Course Webpage
CV
Current CV here (updated September 2024)
Papers
Mellin Transform Formulas for Drinfeld Modules (With O. Gezmis)
Submited for publication, 35 pages (2024) [pdf | arxiv]
A Motivic Pairing and the Mellin Transform in Function Fields
Advances in Mathematics (accepted for publication), 35 pages (2024) [pdf | arxiv]
An Equivariant Tamagawa Number Formula for t-Modules and Applications (With C. Popescu)
Arithmetic of L-series - Proceedings of an international conference held in Madrid, EMS Series of Congress Reports, European Mathematical Society Press. (accepted for publication) [pdf | arxiv]
On log-algebraic identities for Anderson t-modules and characteristic p multiple zeta values (With T. Ngo Dac)
IMRN, Volume 2023, Issue 16, August 2023, Pages 13687–13756 [pdf | arxiv]
Algebraic Relations Among Special Zeta Values on Elliptic Curves (With T. Ngo Dac)
Forum of Mathematics, Sigma 2023; 11:e90. doi:10.1017/fms.2023.94 [pdf | arxiv]
An Equivariant Tamagawa Number Formula for Drinfeld Modules and Applications (With J. Ferrara, Z. Higgins and C. Popescu)
Algebra and Number Theory, Vol. 16 (2022), No. 9, 2215–2264, DOI: 10.2140/ant.2022.16.2215 [pdf | arxiv]
Taylor Coefficients of t-Motivic Multiple Zeta Values and Explicit Formulae (With C. Y. Chang and Y. Mishiba)
Math. Annalen, (2020), 379(2):1-50. [journal | arxiv]
Special zeta values using tensor powers of Drinfeld modules
Math. Res. Letters, vol. 26, (2019), no. 6, 1629 – 1676. [journal | arxiv]
Note: This version contains a couple extra details in the proof of Theorem 6.2 compared to the published version.
Tensor powers of rank 1 Drinfeld modules and periods
Journal of Number Theory (accepted for publication), 28 pages (2019) [pdf | arxiv]
Tensor powers of Drinfeld modules and zeta values
Ph.D. thesis, Texas A&M University (2018) [pdf]
Special L-values and shtuka functions for Drinfeld modules on elliptic curves (with M. Papanikolas)
Research in the Mathematical Sciences (RMS), 5 (2018), no. 1, Paper No. 4, 47 pp. [journal | arxiv]
Integral traces of weak Maass forms of genus zero (with P. Jenkins)
The Ramanujan Journal, (2016), 1-26 [journal | arxiv]
Singular moduli for a distinguished non-holomorphic modular function (with V. Dose, M. Griffin, T. Mao, L. Rolen, L. Willis)
Proc. Amer. Math. Soc. 143 (2015), no. 3, 965-972 [journal]