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Results tagged with nt.number-theory
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user 12160
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
6
votes
1
answer
421
views
Distribution of a function in an arithmetic progression
I am going to have to borrow the opening passage from Bombieri, Friedlander, Iwaniec${}^*$ since they state this idea so well. In the following $\|f\|$ means $\big(\sum_{n\leqslant x} |f(n)|^2\big)^{1 …
- 489
4
votes
1
answer
2k
views
When is the Siegel-Walfisz theorem non-trivial?
The following paragraph appears in Analytic Number Theory (Iwaniec, Kowalski):
The Siegel-Walfisz theorem asserts that:
$\displaystyle \hspace{5cm} \psi(x;q,a) = \frac{x}{\phi(q)} + O(x(\log x)^{- …
- 489
7
votes
1
answer
1k
views
Is it possible to improve on Siegel's theorem for exceptional zeroes?
Let $\chi$ be a real nonprincipal character modulo $q$. Siegel's theorem on exceptional zeroes states that for any $\epsilon >0$ there exists a positive number $C(\epsilon)$ such that, for any real ze …
- 489
17
votes
6
answers
5k
views
A non-technical account of the Birch—Swinnerton-Dyer Conjecture
I was wondering whether anyone knows of any good non-technical or even popular expositions of the Birch—Swinnerton-Dyer conjecture, for someone with minimal background in elliptic curves. I was thinki …
- 489