| dc.creator |
Mazur, Barry |
|
| dc.date |
2019-01-14T13:53:25Z |
|
| dc.date |
2011-05-01 |
|
| dc.date |
2019-01-14T13:53:25Z |
|
| dc.date.accessioned |
2022-05-18T11:03:57Z |
|
| dc.date.available |
2022-05-18T11:03:57Z |
|
| dc.identifier |
Mazur, Barry. 2011. “How Can We Construct Abelian Galois Extensions of Basic Number Fields?” Bulletin of the American Mathematical Society 48 (2): 155–155. https://doi.org/10.1090/s0273-0979-2011-01326-x. |
|
| dc.identifier |
0273-0979 |
|
| dc.identifier |
1088-9485 |
|
| dc.identifier |
http://nrs.harvard.edu/urn-3:HUL.InstRepos:37989549 |
|
| dc.identifier |
10.1090/s0273-0979-2011-01326-x |
|
| dc.identifier.uri |
http://localhost:8080/xmlui/handle/CUHPOERS/26597 |
|
| dc.description |
Irregular primes-37 being the first such prime-have played a great role in number theory. This article discusses Ken Ribet's construction-for all irregular primes p-of specific abelian, unramified, degree p extensions of the number fields Q(e(2 pi i/p)). These extensions with explicit information about their Galois groups (they are Galois over Q) were predicted to exist ever since the work of Herbrand in the 1930s. Ribet's method involves a tour through the theory of modular forms; it demonstrates the usefulness of congruences between cuspforms and Eisenstein series, a fact that has inspired, and continues to inspire, much work in number theory. |
|
| dc.description |
Mathematics |
|
| dc.description |
Version of Record |
|
| dc.format |
application/pdf |
|
| dc.language |
en_US |
|
| dc.publisher |
American Mathematical Society (AMS) |
|
| dc.relation |
http://www.ams.org/bull/2011-48-02/S0273-0979-2011-01326-X/S0273-0979-2011-01326-X.pdf |
|
| dc.relation |
Bulletin of the American Mathematical Society |
|
| dc.source |
Bull. Amer. Math. Soc. |
|
| dc.title |
How Can We Construct Abelian Galois Extensions of Basic Number Fields? |
|
| dc.type |
Journal Article |
|