Results 101 to 110 of about 2,736 (131)

Note on equality of L -functions of elliptic curves

Archiv der Mathematik, 1998
We study the equality L(A, K, s)=L(B, M, s) where A, B are elliptic curves defined over Q, and K, M Galois number fields. Using Faltings theorem on isogenies of abelian varieties, Serre theorem on supersingular reduction of elliptic curves and properties of Weil functor of restriction of scalars, the equality is described completely.
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Value distribution of twists of L-functions of elliptic curves

Proceedings of the Steklov Institute of Mathematics, 2017
The paper is devoted to the universality of \(L\)-functions associated with elliptic curves. Let \(E\) be an elliptic curve over the field of rational numbers defined by the Weierstrass equation \[ y^2=x^3+ax+b,\qquad a,b\in \mathbb{Z}, \] with nonzero discriminant \(\Delta=-16(4a^3+27b^2)\). Given a prime \(p\), denote by \(E_p\) the reduction modulo \
Laurinčikas, Antanas, Macaitiene, Renata   +1 more
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Limit theorems for twists of L-functions of elliptic curves

Lithuanian Mathematical Journal, 2010
For \(Q \geq 2\) let \(M_Q\) denote the number of all distinct, non-principal Dirichlet characters \(\chi (\neq \chi_0)\) with modulus \(q\), such that \(q \leq Q\). Let \(P_Q\) denote the probability measure defined on Borel subsets \(A\) of \(\mathbb{R}\) by \[ P_Q(A)=\frac{1}{M_Q}\cdot \text{Card} \left(\{ \chi = \chi \pmod q,\, \chi \neq \chi_0 : q
Garbaliauskienė, V., Laurinčikas, A., Stankus, E.   +2 more
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L-Functions of Universal Elliptic Curves Over Igusa Curves

American Journal of Mathematics, 1990
This paper is concerned with computing the L-functions of the title in terms of modular forms. Because one can produce zeros of these L-functions, they seem to provide interesting test cases for various conjectures relating L-functions to cycles. In the first three sections we state the theorem, review some consequences, and give a brief sketch of the ...
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An Elliott-type theorem for twists of L-functions of elliptic curves

Mathematical Notes, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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L-Functions of Elliptic Curves and Modular Forms

2004
In the previous chapter we examined representations of Galois groups of global fields into GL(n, ℂ), and their L-functions. Such representations are necessarily of finite image. We saw at the end that an important example is supplied by modular forms of weight 1.
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The Hasse—Weil L-Function of an Elliptic Curve

1984
At the end of the last chapter, we used reduction modulo p to find some useful information about the elliptic curves E n : y 2 = x 3 -- n 2 x and the congruent number problem.
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Elliptic Curve Cryptography; Applications, challenges, recent advances, and future trends: A comprehensive survey

Computer Science Review, 2023
Shamsher Ullah
exaly  

L-Function of an Elliptic Curve and Its Analytic Continuation

1987
We introduce the L-function of an elliptic curve E over a number field and derive its elementary convergence properties. An L-function of this type was first introduced by Hasse, and the concept was greatly extended by Weil. For this reason it is frequently called the Hasse-Weil L-function.
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Double image encryption algorithm based on compressive sensing and elliptic curve

AEJ - Alexandria Engineering Journal, 2022
Guo-dong Ye
exaly