bio | website | marksapir.wordpress.com |
---|---|---|
location | Nashville, TN | |
age | ||
visits | member for | 5 years, 2 months |
seen | Aug 27 at 2:35 | |
stats | profile views | 29,905 |
Professor of Mathematics at Vanderbilt University
Aug
28 |
awarded | Necromancer |
Jul
25 |
awarded | Nice Answer |
Jun
22 |
awarded | Yearling |
Jun
6 |
awarded | Nice Answer |
May
10 |
reviewed | Leave Open Which operators other than self-adjoint operators have no purely imaginary eigenvalues? |
May
10 |
reviewed | Leave Open quantum deformation |
May
10 |
comment |
Class field towers
@FranzLemmermeyer Your and David Loeffler's comments do help finding true motivation for the class tower problem. Thanks! |
Apr
24 |
comment |
Class field towers
@quid Yes, it is the same paper, published in Abh. Math. Semin. Univ. Hambg. (2009) 79: 165–187. |
Apr
24 |
comment |
Class field towers
@quid I looked at that discussion. As far as I understand from Lemmermeyer's paper (the link on that page is broken, but I found the paper anyway), it is more about ideals and their unique prime decompositions, i.e., class number 1, than about general class number. It is good to know that reciprocity laws played important role in the development of the theory of ideal numbers. I did not know that before. FLT also played a role, whether decisive or not - it is not that important to me. |
Apr
24 |
awarded | Nice Question |
Apr
23 |
revised |
Class field towers
Corrected a misprint in the second line. |
Apr
23 |
comment |
Class field towers
Thank you! It does make sense. But at least FLT was the main reason for defining the class number. Right? |
Apr
23 |
comment |
Class field towers
The question was more about motivation. I always thought that FLT was the motivation for the class tower problem. But it looks like there is no close relation. |
Apr
23 |
accepted | Class field towers |
Apr
23 |
comment |
Class field towers
Thank you very much! |
Apr
23 |
comment |
Class field towers
@DavidLoeffler: If the class number of $\mathbb{Q}[\zeta]$ is 1, $\zeta^n=1$, then FLT for that $n$ follows, right? Isn't it enough to assume that $\zeta$ is inside a number field with class number 1? |
Apr
23 |
comment |
Class field towers
@DavidLoeffler: Would the case when $p$ is prime imply FLT? |
Apr
23 |
asked | Class field towers |
Apr
10 |
comment |
Can an algebraic number on the unit circle have a conjugate with absolute value different from 1?
As I said, the coefficients are algebraic integers and stable under the action of the Galois group. Hence these coefficients are rational integers. What's wrong? |
Apr
9 |
comment |
Can an algebraic number on the unit circle have a conjugate with absolute value different from 1?
@YCor: Do you know what Vieta's formulas are, en.wikipedia.org/wiki/Vieta%27s_formulas ? I have edited the answer making it more accessible. |