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Results tagged with nt.number-theory
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user 7313
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
10
votes
2
answers
1k
views
Class number of real maximal subfield of cyclotomic fields
Let $p$ be a prime number and $h_p^+$ the class number of $\mathbb{Q}(\zeta_p + \zeta_p^{-1})$. What is known about the values of $p$ for which $h_p^+ = 1$?
Are there infinitely many? Finitely many? …
- 1,271
7
votes
3
answers
3k
views
Atkin-Lehner involution and class number
I was told of a relation between the number of fixed points of the Atkin-Lehner involution and the class number of certain number fields.
Can someone point me to a reference where I could learn about …
- 1,271
3
votes
2
answers
3k
views
Units in cyclotomic fields
Let $q$ and $r$ be distinct prime numbers. I noticed (computing a few cases) that $\zeta_{2q} + \zeta_{2q}^{-1} + \zeta_{2r} + \zeta_{2r}^{-1}$ is a unit (in $\mathbb{Z}[\zeta_{2qr}]$, say). Is this a …
- 1,271
0
votes
0
answers
735
views
Igusa model of modular curves
I would like to know what the "Igusa model" of the modular curve is and basic properties about it.
Can someone point me to a reference?
- 1,271