Results 31 to 40 of about 2,736 (131)
A Discrete Limit Theorem for L-Functions of Elliptic Curves
Jaunųjų mokslininkų darbai, 2018 In the paper, we prove the discrete limit theorem in the sense of the weak convergence of probability measures in the space of analytic on DV = {s ∈ C : 1 < σ < 3/2, |t| < V} functions for L-functions of elliptic curves LE(s). The main statement of the paper is as follows.
Virginija Garbaliauskienė +1 more
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A Weighted Universality Theorem for L-Functions of Elliptic Curves
Jaunųjų mokslininkų darbai, 2018 In the paper, a short survey on universality results for L-functions of elliptic curves over the field of rational numbers is given and weighted universality theorem is proven. All stated universality theorems are of continuous type. The proof of the universality for L-functions of elliptic curves is based on a limit theorem in the sense of weak ...
Antanas Garbaliauskas +1 more
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Determination of elliptic curves by their adjoint p-adic L-functions
Journal of Number Theory, 2015 Fix $p$ an odd prime. Let $E$ be an elliptic curve over $\mathbb{Q}$ with semistable reduction at $p$. We show that the adjoint $p$-adic $L$-function of $E$ evaluated at infinitely many integers prime to $p$ completely determines up to a quadratic twist the isogeny class of $E$.
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Euler Product Asymptotics for L-functions of Elliptic Curves
International Mathematics Research NoticesAbstract Let $E/\mathbb Q$ be an elliptic curve and for each prime $p$, and let $N_{p}$ denote the number of points of $E$ modulo $p$. The original version of the Birch and Swinnerton-Dyer conjecture asserts that $\prod \limits _{p \leq x} \frac{N_{p}}{p} \sim C (\log x)^{\textrm{rank}(E(\mathbb Q))}$ as $x \to \infty $.
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OnL-functions of elliptic curves and anticyclotomic towers
Inventiones Mathematicae, 1984 Let \(K\) be an imaginary quadratic number field. Let \(P\) be a finite set of prime numbers, and let \(L\) be the maximal anticyclotomic extension of \(K\) unramified outside \(P\). Let \(E\) be an elliptic curve defined over \(\mathbb Q\) which has complex multiplication by the ring of integers in \(K\). Let \(V=\mathbb C\otimes E(L)\) where \(E(L)\)
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OnL-functions of elliptic curves and cyclotomic towers
Inventiones Mathematicae, 1984 Let \(f\) be a normalized new form of weight 2, character \(\psi\), and level \(N\). Let \(P\) be a finite set of primes not dividing \(N\), and let \(X\) be the set of all primitive Dirichlet characters which are unramified outside \(P\) and infinity. For \(\chi\in X\), let \(L(s,f,\chi)\) be the \(L\)-function attached to \(f\) and \(\chi\). The main
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On the low-lying zeros of Hasse–Weil L-functions for elliptic curves
Advances in Mathematics, 2008 In this paper, we obtain an unconditional density theorem concerning the low-lying zeros of Hasse-Weil L-functions for a family of elliptic curves. From this together with the Riemann hypothesis for these L-functions, we infer the majorant of 27/14 (which is strictly less than 2) for the average rank of the elliptic curves in the family under ...
Baier, S, Zhao, L
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On the Generalizations of Universality Theorem for L-Functions of Elliptic Curves
Jaunųjų mokslininkų darbai, 2017 In the paper, the continuous type’s universality theorem for L-functions of elliptic curves is discussed and its generalizations in three directions – for positive integer powers and derivatives of L-functions of elliptic curves as well as the weighted universality theorem of L-functions of elliptic curves – are given.
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Deninger's conjecture onL-functions of elliptic curves ats=3
Journal of Mathematical Sciences, 1996 LaTeX
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Discrete universality theorem for l-functions of elliptic curves
, 2010 Let E be an elliptic curve over the field of rational numbers Q defined by the Weierstrass equation y2 = x3 + ax+b, x3 + ax + b, aa,, bb ∈Z Z. Denote by Δ = –16(4a3 + 27b2) the discriminant of the curve E, and suppose that Δ ≠ 0. Then the roots of the cubic x3 + ax+b are distinct, and the curve E is non-singular.
Čeponienė, Jurgita +2 more
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