منابع مشابه
On the arithmetic dimension of triangle groups
Let ∆ = ∆(a, b, c) be a hyperbolic triangle group, a Fuchsian group obtained from reflections in the sides of a triangle with angles π/a, π/b, π/c drawn on the hyperbolic plane. We define the arithmetic dimension of ∆ to be the number of split real places of the quaternion algebra generated by ∆ over its (totally real) invariant trace field. Takeuchi has determined explicitly all triples (a, b,...
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Let Pf (N ) be the set of finite nonempty subsets of N and for F,G ∈ Pf (N ) write F < G when maxF < minG. Let X = {(F,G) : F,G ∈ Pf (N ) and F < G}. A triangle in X is a set of the form {(F ∪ H,G), (F,G), (F,H ∪ G)} where F < H < G. Motivated by a question of Erdős, Nešetŕıl, and Rödl regarding three term arithmetic progressions, we show that any finite subset Y of X contains a relatively larg...
متن کاملAn Arithmetic Analogue of Fox's Triangle Removal Argument
We give an arithmetic version of the recent proof of the triangle removal lemma by Fox [Fox11], for the group Fn 2 . A triangle in Fn 2 is a triple (x, y, z) such that x + y + z = 0. The triangle removal lemma for Fn 2 states that for every ε > 0 there is a δ > 0, such that if a subset A of Fn 2 requires the removal of at least ε · 2n elements to make it triangle-free, then it must contain at l...
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Let PSL2(R) be a cocompact arithmetic triangle group, i.e. a triangle Fuchsian group that arises from the unit group of a quaternion algebra over a totally real number eld. We introduce CM points de ned on the Shimura curve quotient XC = nH, and we algorithmically apply the Shimura reciprocity law to compute these points and their Galois conjugates so as to recognize them as purported algebraic...
متن کاملA tight bound for Green's arithmetic triangle removal lemma in vector spaces
Let p be a fixed prime. A triangle in Fp is an ordered triple (x, y, z) of points satisfying x + y + z = 0. Let N = p, (the size of Fp ). Green proved an arithmetic triangle removal lemma which says that for every > 0 and prime p, there is a δ > 0 such that if X, Y , and Z are subsets of Fp and the number of triangles in X × Y ×Z is at most δN (so a δ fraction of all possible triangles), then w...
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ژورنال
عنوان ژورنال: Journal of Mathematics Research
سال: 2017
ISSN: 1916-9809,1916-9795
DOI: 10.5539/jmr.v9n2p100