現代数学の系譜工学物理雑談古典ガロア理論も読む49

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574: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [sage] 2018/01/18(木) 23:11:47.44 ID:gGT+ehE7

>>570 補足

Swinnerton-Dyerさんが出てくるね（＾＾

https://en.wikipedia.org/wiki/Littlewood_conjecture
Littlewood conjecture
(抜粋)
Connection to further conjectures[edit]
It is known that this would follow from a result in the geometry of numbers, about the minimum on a non-zero lattice point of a product of three linear forms in three real variables: the implication was shown in 1955 by J. W. S. Cassels and Swinnerton-Dyer.[1]
This can be formulated another way, in group-theoretic terms. There is now another conjecture, expected to hold for n ? 3: it is stated in terms of G = SLn(R), Γ = SLn(Z), and the subgroup D of diagonal matrices in G.

Conjecture: for any g in G/Γ such that Dg is relatively compact (in G/Γ), then Dg is closed.

This in turn is a special case of a general conjecture of Margulis on Lie groups.
(引用終り)

https://en.wikipedia.org/wiki/Peter_Swinnerton-Dyer
Peter Swinnerton-Dyer
(抜粋)
Sir Henry Peter Francis Swinnerton-Dyer, 16th Baronet KBE FRS (born 2 August 1927), commonly known as Peter Swinnerton-Dyer, is an English mathematician specialising in number theory at University of Cambridge.
As a mathematician he is best known for his part in the Birch and Swinnerton-Dyer conjecture relating algebraic properties of elliptic curves to special values of L-functions, which was developed with Bryan Birch during the first half of the 1960s with the help of machine computation, and for his work on the Titan operating system.
(引用終り)

https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture
Birch and Swinnerton-Dyer conjecture

http://rio2016.5ch.net/test/read.cgi/math/1514376850/574

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