All Questions
Tagged with motivation nt.number-theory
9 questions
18
votes
4
answers
2k
views
What's the use of group cohomology for class field theory?
I'm a graduate student studying now for the first time class field theory.
It seems that how to teach class field theory is a problem over which many have already written on MathOverflow.
For example ...
- 521
9
votes
3
answers
2k
views
Simple motivation to study arithmetic geometry
Is there a simple-to-understand diophantine equation (in the sense that it's easy to explain to a child) that has a positive integer solution, but to prove that such a solution exists and to find it ...
- 649
11
votes
2
answers
1k
views
What is the significance of Friedlander-Iwaniec and related theorems?
On p.177 of Number Theory Revealed: A Masterclass by Andrew Granville, the author states that "One can ask for prime values of polynomials in two or more variables." (though he later ...
- 2,075
26
votes
1
answer
4k
views
Why did Euler consider the zeta function?
Many zeta functions and L-functions which are generalizations of the Riemann zeta function play very important roles in modern mathematics (Kummer criterion, class number formula, Weil conjecture, BSD ...
- 293
40
votes
6
answers
4k
views
What motivations for automorphic forms?
Automorphic forms are ubiquitous in modern number theory and stands as a mysterious Graal lying at the intersection of many fields, if not building valuable bridges between them. However, since this ...
296
votes
8
answers
143k
views
Philosophy behind Mochizuki's work on the ABC conjecture
Mochizuki has recently announced a proof of the ABC conjecture. It is far too early to judge its correctness, but it builds on many years of work by him. Can someone briefly explain the philosophy ...
14
votes
1
answer
5k
views
Why are Galois Representations so important in Number theory ?
Dear everyone,
Motivation :
From the past few days, I have been reading about the Galois Representations . I was really amazed to see that every seminal idea in the theory of elliptic curves have ...
12
votes
6
answers
3k
views
applications of Tate-Poitou duality
What are nice applications of Tate-Poitou duality?
12
votes
3
answers
1k
views
Motivation for uniform surjectivity of mod l representations associated to elliptic curves
Background
Let $E$ be an elliptic curve over $\mathbb{Q}$ and let $G_{\mathbb{Q}}$ be the absolute Galois group $Aut(\overline{\mathbb{Q}})$. For any positive integer $n$ the $n$-torsion subgroup $E[...
- 10.5k