Four exponentials conjecture of Drinfeld modules
Author:
Mao-Sheng Li
Journal:
Proc. Amer. Math. Soc. 149 (2021), 2375-2380
MSC (2020):
Primary 11J81, 11J93; Secondary 11T55
DOI:
https://doi.org/10.1090/proc/15389
Published electronically:
March 29, 2021
MathSciNet review:
4246790
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Based on the algebraic independence of Drinfeld logarithms at algebraic points proved by Chang and Papanikolas, we show the four exponentials conjecture of Drinfeld modules, by following the typical approach in the classical transcendental number theory.
- L. Alaoglu and P. Erdös, On highly composite and similar numbers, Trans. Amer. Math. Soc. 56 (1944), 448–469. MR 11087, DOI https://doi.org/10.1090/S0002-9947-1944-0011087-2
- Leonard Carlitz, On certain functions connected with polynomials in a Galois field, Duke Math. J. 1 (1935), no. 2, 137–168. MR 1545872, DOI https://doi.org/10.1215/S0012-7094-35-00114-4
- Chieh-Yu Chang and Matthew A. Papanikolas, Algebraic independence of periods and logarithms of Drinfeld modules, J. Amer. Math. Soc. 25 (2012), no. 1, 123–150. With an appendix by Brian Conrad. MR 2833480, DOI https://doi.org/10.1090/S0894-0347-2011-00714-5
- V. G. Drinfel′d, Elliptic modules, Mat. Sb. (N.S.) 94(136) (1974), 594–627, 656 (Russian). MR 0384707
- David Goss, Basic structures of function field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 35, Springer-Verlag, Berlin, 1996. MR 1423131
- Serge Lang, Introduction to transcendental numbers, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0214547
- Matthew A. Papanikolas, Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms, Invent. Math. 171 (2008), no. 1, 123–174. MR 2358057, DOI https://doi.org/10.1007/s00222-007-0073-y
- Jing Yu, A six exponentials theorem in finite characteristic, Math. Ann. 272 (1985), no. 1, 91–98. MR 794093, DOI https://doi.org/10.1007/BF01455930
- Michel Waldschmidt, Diophantine approximation on linear algebraic groups, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 326, Springer-Verlag, Berlin, 2000. Transcendence properties of the exponential function in several variables. MR 1756786
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2020): 11J81, 11J93, 11T55
Retrieve articles in all journals with MSC (2020): 11J81, 11J93, 11T55
Additional Information
Mao-Sheng Li
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
Address at time of publication:
Department of Physics, Southern University of Science and Technology, Shenzhen 518055, People’s Republic of China
MR Author ID:
1165789
ORCID:
0000-0002-0150-8004
Email:
li.maosheng.math@gmail.com
Keywords:
Four exponentials conjecture,
transcendence,
Drinfeld modules
Received by editor(s):
January 29, 2020
Received by editor(s) in revised form:
January 31, 2020, August 13, 2020, and October 8, 2020
Published electronically:
March 29, 2021
Additional Notes:
The author would like to thank the National Natural Science Foundation of China (Grants No. 11371210, 11871295, and 12005092) for partial financial support.
Communicated by:
Matthew Papanikolas
Article copyright:
© Copyright 2021
American Mathematical Society
