Tagged Questions
21
votes
3answers
360 views
Intuition for the Importance of Modular Forms
I am learning about modular forms for the first time this term and am just starting to wrap my head around what might be the big picture of things.
I was wondering if the following interpretation of ...
2
votes
2answers
103 views
How do you find the closed form of these recurrence relations?
I found these two recurrence relations in an old textbook and was hoping someone could show me how to solve them for their closed form. If not, a final answer would also be appreciated, as it helps ...
8
votes
5answers
314 views
Arithmetic of irrationals and the Vedanta behind it..
I am really curious about the Vedanta behind the arithmetic operations on irrational numbers. It still got aggrevated after the productive discussions with my friend. So I decided to ask it here.
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6
votes
1answer
215 views
What is the intuitive meaning of “conspiracy” in number theory?
Assuming very little number-theoretic background from my part, could you please explain me what is the intuitive meaning behind "conspiracy" in number theory? There is no formal entry on Wikipedia and ...
4
votes
1answer
316 views
Subset of natural numbers such that any natural number except 1 can be expressed as sum of two elements
Let $X$ be the set of natural numbers $k_i$, $k_i \geq 1$, with the property that at least one of the equations $p_i = $6$ k_i \pm 1$ gives the $i$-th prime number (disregarding $2$ and $3$), and ...
10
votes
1answer
842 views
What is the intuition behind the concept of Tate twists?
For any field $K$ we can define the cyclotomic character $\chi: \operatorname{Gal}(K)\rightarrow GL_1(\hat{\mathbb{Z}})$. For any representation $V$ (I will view this as a module over ...
32
votes
1answer
550 views
How does one see Hecke Operators as helping to generalize Quadratic Reciprocity?
My question is really about how to think of Hecke operators as helping to generalize quadratic reciprocity.
Quadratic reciprocity can be stated like this: Let $\rho: Gal(\mathbb{Q})\rightarrow ...
4
votes
1answer
352 views
Largest known integer
Does there exist a property which is known to be satisfied by only one integer, but such that this property does not provide a means by which to compute this number? I am asking because this number ...
12
votes
3answers
586 views
What is the intuition behind Gauss sums?
Let $ \chi $ be a character on the field $ F_p $, and fix some $a \in F_p $.
We define a Gauss sum to be:
$g_a (\chi) = \sum_{t\in F_p}\chi(t)\zeta^{at}$ where $\zeta$ is a primitive $p^{th}$ root of ...
19
votes
4answers
850 views
You are standing at the origin of an “infinite forest” holding an “infinite bb-gun”
I use stories like these to develop intuition... or perhaps to destroy it. I have my own answers in mind, but I want to see if I have made any mistakes...
You are standing at the origin of an ...
