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john mangual
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Nov
25
accepted
What is the orthonormal basis for the Bergman space on the disk?
Nov
25
awarded
Popular Question
Nov
24
awarded
Nice Question
Nov
23
revised
Is there any pattern to the continued fraction of $\sqrt[3]{2}$?
added 1501 characters in body; edited title
Nov
23
comment
Is there any pattern to the continued fraction of $\sqrt[3]{2}$?
@ToddTrimble they say "However, such a formula does not necessarily usefully increase our understanding of the nature of the partial quotients of such a number."
Nov
23
comment
Is there any pattern to the continued fraction of $\sqrt[3]{2}$?
@ToddTrimble the question is deliberately vague. the continued fraction digits of $\sqrt[3]{2}$ can't repeat. so we need to find some other notion of pattern.
Nov
23
asked
Is there any pattern to the continued fraction of $\sqrt[3]{2}$?
Nov
22
accepted
How does the solenoid structure of $\mathbb{A}/\mathbb{Q}$ lift to $PGL(2, \mathbb{A})/ PGL(2, \mathbb{Q})$?
Nov
19
accepted
Proving Legendre's Sum of 3 Squares Theorem via Geometry of Numbers
Nov
18
comment
Proving Legendre's Sum of 3 Squares Theorem via Geometry of Numbers
I notice
Dirichlet's Theorem
on prime numbers in arithmetic progressions is an input. So for example there are infinitely many prime numbers among $1,4,7,10,\dots$. And
Quadratic Reciprocity
of
Legendre Symbols
that $\left(\frac{p}{q}\right)\left(\frac{q}{p}\right) = (-1)^{\frac{p-1}{2}\frac{q-1}{2}}$ is also an input.
Nov
18
comment
Proving Legendre's Sum of 3 Squares Theorem via Geometry of Numbers
thanks this is
much
shorter than what I was about to attempt
Nov
18
comment
Proving Legendre's Sum of 3 Squares Theorem via Geometry of Numbers
@so-calledfriendDon there must be tons of places I haven't looked but I can't go on forever so I am putting it on here. Also found this
math.uga.edu/~pete/geometryofnumbers.pdf
Nov
18
asked
Proving Legendre's Sum of 3 Squares Theorem via Geometry of Numbers
Nov
3
awarded
Nice Answer
Nov
1
awarded
Yearling
Oct
22
accepted
Distribution of the Error term in GH Hardy's “curious result” $\sum_{\nu \leq n } \{ \nu \theta \}^2 = \tfrac{1}{12} n + O(1)$
Oct
22
revised
Distribution of the Error term in GH Hardy's “curious result” $\sum_{\nu \leq n } \{ \nu \theta \}^2 = \tfrac{1}{12} n + O(1)$
added 374 characters in body
Oct
21
awarded
Nice Question
Oct
20
revised
Distribution of the Error term in GH Hardy's “curious result” $\sum_{\nu \leq n } \{ \nu \theta \}^2 = \tfrac{1}{12} n + O(1)$
added 202 characters in body
Oct
20
comment
Distribution of the Error term in GH Hardy's “curious result” $\sum_{\nu \leq n } \{ \nu \theta \}^2 = \tfrac{1}{12} n + O(1)$
When $\theta$ is irrational this result should hold except for the size of error term. So it's $\frac{1}{12}n$ and some change. And we debate the size of the chance
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