The Mahler measure and \(K_2\) of elliptic curves. (English) Zbl 1397.11093
Cheng, Shiu-Yuen (ed.) et al., Introduction to modern mathematics. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-305-0/pbk). Advanced Lectures in Mathematics (ALM) 33, 227-245 (2015).
Summary: There are deep relations between the Mahler measures of certain two variables polynomials and \(L\)-values of the curves defined by the polynomials. The first progress was made by Deninger in 1997. Then Boyd made hundreds of conjectures on this topic. In recent years, many conjectures were proved. This note will give a survey mainly on the work of Bertolini and Darmon, Boyd, Brunalt, Deninger Lalin, Rogers and Zudilin etc. in this area. We also introduce our work (with Ji) in progress.
For the entire collection see [Zbl 1326.00080].
For the entire collection see [Zbl 1326.00080].
MSC:
| 11G05 | Elliptic curves over global fields |
| 11-02 | Research exposition (monographs, survey articles) pertaining to number theory |
| 11G30 | Curves of arbitrary genus or genus \(\ne 1\) over global fields |
| 19E08 | \(K\)-theory of schemes |
