The Sato-Tate conjecture
نویسندگان
چکیده
منابع مشابه
The Sato - Tate Conjecture for Modular Forms of Weight 3
We prove a natural analogue of the Sato-Tate conjecture for modular forms of weight 2 or 3 whose associated automorphic representations are a twist of the Steinberg representation at some finite place. 2000 Mathematics Subject Classification: 11F33.
متن کاملThe Sato-tate Conjecture for Modular Forms of Weight
We prove a natural analogue of the Sato-Tate conjecture for modular forms of weight 2 or 3 whose associated automorphic representations are a twist of the Steinberg representation at some finite place.
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1 Acknowledgments I'm greatly thankful to William Stein, of course, not only for his patience and support while completing my thesis work, but especially for opening up so many opportunities for me to contribute to current research related to the topic of this paper. Thank you for including me in your correspondences with the " big players " in number theory. Thank you to Jim Morrow for his ass...
متن کاملThe Error Term in the Sato-tate Conjecture
Let f(z) = ∑∞ n=1 a(n)e 2πinz ∈ S k (Γ0(N)) be a newform of even weight k ≥ 2 that does not have complex multiplication. Then a(n) ∈ R for all n, so for any prime p, there exists θp ∈ [0, π] such that a(p) = 2p(k−1)/2 cos(θp). Let π(x) = #{p ≤ x}. For a given subinterval I ⊂ [0, π], the now-proven Sato-Tate Conjecture tells us that as x→∞, #{p ≤ x : θp ∈ I} ∼ μST (I)π(x), μST (I) = ∫
متن کاملSato-Tate distributions
be the trace of Frobenius. By a theorem of Hasse, each normalized trace xp := ap/ p p is a real number in the interval [−2, 2]. The xp vary with p in an apparently unpredictable way, and in the absence of any other information, one might suppose that they should be uniformly distributed over [−2, 2]. A few experiments quickly dispels this notion (here is a typical example), however, the distrib...
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ژورنال
عنوان ژورنال: Current Developments in Mathematics
سال: 2006
ISSN: 1089-6384,2164-4829
DOI: 10.4310/cdm.2006.v2006.n1.a1