On the vanishing of twists of L-functions of elliptic curves Chantal ...
On the vanishing of twists of L-functions of elliptic curves Chantal ...
On the vanishing of twists of L-functions of elliptic curves Chantal ...
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Random matricesKeating and Snaith: statistics on <strong>the</strong> values <strong>of</strong>L f (s) in F should fit those <strong>of</strong> <strong>the</strong> characteristicpolynomials <strong>of</strong> random matrices in G(N).For each A ∈ G(N), letλ 1 = e iθ 1, . . . , λ N = e iθ Nbe <strong>the</strong> eigenvalues <strong>of</strong> A ordered such that0 ≤ θ 1 ≤ . . . ≤ θ N < 2πand letP A (λ) = det (A − λI)be <strong>the</strong> characteristic polynomial <strong>of</strong> A.Notice thatP A (1) = 0 ⇐⇒ λ 1 = e iθ 1 = 1 ⇐⇒ θ 1 = 011
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