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Results tagged with reference-request
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user 8857
This tag is used if a reference is needed in a paper or textbook on a specific result.
1
vote
Reference request: The geometry of $GL_2(\mathbb{R})$ and related questions
You can try to take a look in Dave Witte's book about arithmetic groups here - http://people.uleth.ca/~dave.morris/books/IntroArithGroups.html
He also presents in his site a dynamical approach to this …
2
votes
Gauss sums over multiplicative subgroups
A very readable introduction is Kurlberg's paper - http://www.math.kth.se/~kurlberg/eprints/short_expsum.pdf
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5
votes
Accepted
Kronecker theorems on linear forms.
Take a look at Cassels - "An intorduction to diophantine approximation", Theorem VI in Ch1, where the theorem that Gerry mentioned is proved.
I'm guessing that it appears also in Siegel's book about t …
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7
votes
Background for Hejhal's "The Selberg Trace Formula for $PSL(2, \mathbb{R})$
Well, the modern viewpoint relays on the interpretation of "fourier transform" (in any generalized fashion you like to define "fourier transform") in representation-theoretic language.
As a consequenc …
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3
votes
Accepted
Furstenberg-Zimmer theorem: non-invertible systems
Posted as requested - consult the book by Manfred Einsiedler and Tom Ward - "Ergodic Theory with a view towards number theory" - published in GTM, especially in ch 7.
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4
votes
Accepted
Looking for concise books on automorphic L-functions, Eisenstein series on adelic homogeneou...
This is not exactly what you've asked for, but I'll address this article directly, because it is not related to automorphic L-functions "directly" but more to homogeneous dynamics.
You can actually re …
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11
votes
Accepted
Furstenberg $\times 2 \times 3$ conjecture, bibliography
Well that will be some lengthy answer.
The first article that was published after the famous disjointness paper is another paper by Hillel called "Intersections of Cantor sets", it's related to the m …
4
votes
Hausdorff dimension of sequence space
This observation is attributed to H. Furstenberg, and appears (in the case of shift-invariant sets, i.e. Cantor sets) in his beautiful Disjointness paper (in section $3$, which you can read independen …
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8
votes
Applications of measure, integration and Banach spaces to combinatorics
Fourier Analysis is a major tool in Arithmetic combinatorics (see Tao and Vu's book, they have a chapter named L^p theory, i.e. the theorem of Bourgain's about "long APs in sumsets").
Moreover, one c …
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3
votes
Accepted
Does the set of Diophantine $m$-tuples has full measure?
I'm pretty sure that plenty of those kind of questions are covered in Cassels' book.
The modern approach to this kind of problems follows from dynamics on homogeneous spaces via Dani's correspondence …
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2
votes
Geodesics on hyperbolic surfaces whose closures have arbitrary Hausdorff dimension
Show that for a Bernoulli system, there exists ergodic (Bernoulli) measures of any given entropy (between 0 and full entropy). Pick such a measure with appropriate entropy as you would like. Recall t …
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10
votes
Accepted
References on Lie groups and dynamical systems
The connections between Dynamics and Lie Groups (or Algebraic groups) comes mainly in two flavours:
Smooth dynamics, like others have stated Hamiltonian dyanmics and differential equations.
Applicati …
2
votes
Decay of matrix coefficients of non-tempered representation
There is some confusion here, as literally the construction of complementary series in $SL_{2}$ will give you unitary representations with arbitrary slow decay.
For any homogeneous space $G/\Gamma$, t …
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