If A is an elliptic curve over Q, let w(A) ∈ {±1} denote the root number in the functional equation of the L-function L(A, s).
Rank frequencies for quadratic twists of elliptic curves
The resulting equation, which relates the number of dissimilar vertices to the number of dissimilar edges and symmetry-edges in a tree, can be used to derive the generating function for unrooted trees from the generating functions for trees rooted at a vertex, at an edge, or at a symmetry-edge, respectively .
Enumeration of Unlabeled Outerplanar Graphs
S is a principal ideal domain, then there is a model for E given by an equation y 2 = F (x), where the coeﬃcients of F are in oS, the leading coeﬃcient of F is an S -unit, and F does not have multiple roots at any of the ﬁnite places outside of S .
A Shafarevich-Faltings Theorem For Rational Functions
An algorithmic procedure to determine the roots of the characteristic equation has been recently derived by Farkas .
On the weak solutions of the McKendrick equation: Existence of demography cycles
Akhiezer, On a minimum problem in function theory and the number of roots of an algebraic equation inside the unit disc, Izv.
Boundary Nevanlinna-Pick interpolation for generalized Nevanlinna functions
The classical method is based on the fact that the envelope is locally tangent to the family of curves, and by applying the fundamental theorem of envelopes we can derive an equation for the boundary by ﬁnding the roots of the partial derivative with respect to α of the level set formula for the family FC .
The Elliptical Envelope
Black hole solution (36) possesses an event horizon r+, which is the largest root of the equation ∆2 (r+ ) = 0.
Universal regularization prescription for Lovelock AdS gravity
Laszlo’s modiﬁcation in of the Bedford-Fornæss construction addresses both of these concerns: The peak function is deﬁned in terms of the roots of an algebraic equation naturally associated to the homogeneous polynomial P, and there is good control on the regularity of the peak function.
Peak points for pseudoconvex domains: a survey
In fact, as noted in [Bea90, Equation (2.1)], if char K = 0 and f ∈ K [t] is a polynomial of degree m ≥ 2, and if K contains an (m − 1)-st root of the leading coeﬃcient, then there is a linear polynomial µ ∈ K [t] such that µ−1 ◦ f ◦ µ is in normal form.
The Dynamical Mordell-Lang Conjecture
Assume there are inﬁnitely many γ satisfying (a)–(g) such that Cγ is given by an equation y = ζ ϕr γ (x), for some r ≥ 0 and some d-th root of unity ζ, where d | b and gcd(d, a) = 1.
The Dynamical Mordell-Lang Conjecture
The ﬁrst equation means that a graph in H is obtained by substituting every edge in a planar triangulation by an edge-rooted graph whose root does not belong to a triangulation (because of the statement of Wagner’s theorem).
On the number of graphs not containing $K_{3,3}$ as a minor
In this section following Armentano–Dedieu we give an answer to the average number of real roots of a random system of equations expresed in the Bernstein basis.
A review of some recent results on random polynomials over R and over C
Frobenius automorphism of k lifts to an automorphism σ : R We assume that the ﬁeld K contains a root π of the equation X p−1 + p = 0 (so that it contains all of them).
Product formula for p-adic epsilon factors
The discriminant (i.e. an expression under the root sign in Eq. 11b) of the solved quadratic equation has to be positive for existing ray intersection with the sphere and is just equal to zero for tangential incidence.
Analysis of ellipsometric data obtained from curved surfaces
On the contrary, in the microlocal zone µ > 0, even is pϕ is elliptic, only one of its root in ξn has negative imaginary part and elliptic estimates would only get an equation on the traces of g .
Carleman estimates for the Zaremba Boundary Condition and Stabilization of Waves
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