Results 21 to 30 of about 142 (36)
Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients [PDF]
, 2015 We show that for any ϵ > 0 and a sufficiently large cube-free q, any reduced residue class modulo q can be represented as a product of 14 integers from the interval [1, q1/4,e1/2 + ϵ].
Balog +6 more
core +2 more sources
The frequency of elliptic curve groups over prime finite fields [PDF]
, 2015 Letting $p$ vary over all primes and $E$ vary over all elliptic curves over the finite field $\mathbb{F}_p$, we study the frequency to which a given group $G$ arises as a group of points $E(\mathbb{F}_p)$.
Chandee, Vorrapan +3 more
core +1 more source
On the de Rham and p-adic realizations of the Elliptic Polylogarithm for CM elliptic curves [PDF]
, 2008 In this paper, we give an explicit description of the de Rham and p-adic polylogarithms for elliptic curves using the Kronecker theta function. We prove in particular that when the elliptic curve has complex multiplication and good reduction at p, then ...
Bannai, Kenichi +2 more
core +2 more sources
Congruences of models of elliptic curves
, 2013 Let O_K be a discrete valuation ring with field of fractions K and perfect residue field. Let E be an elliptic curve over K, let L/K be a finite Galois extension and let O_L be the integral closure of O_K in L.
Liu, Qing, Lu, Huajun
core +3 more sources
On the Birch-Swinnerton-Dyer quotients modulo squares
, 2006 Let A be an abelian variety over a number field K. An identity between the L-functions L(A/K_i,s) for extensions K_i of K induces a conjectural relation between the Birch-Swinnerton-Dyer quotients.
Birch +17 more
core +4 more sources
Elliptic nets and elliptic curves
, 2010 An elliptic divisibility sequence is an integer recurrence sequence associated to an elliptic curve over the rationals together with a rational point on that curve.
Ayad +5 more
core +1 more source
Integral points on elliptic curves and explicit valuations of division polynomials
, 2014 Assuming Lang's conjectured lower bound on the heights of non-torsion points on an elliptic curve, we show that there exists an absolute constant C such that for any elliptic curve E/Q and non-torsion point P in E(Q), there is at most one integral ...
David +15 more
core +1 more source
, 2016 The paper introduces the notions of an elliptic pair, an elliptic cycle and an elliptic list over a square free positive integer d. These concepts are related to the notions of amicable pairs of primes and aliquot cycles that were introduced by Silverman
Babinkostova, Liljana +4 more
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$p$-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas
, 2014 Consider an elliptic curve defined over an imaginary quadratic field $K$ with good reduction at the primes above $p\geq 5$ and has complex multiplication by the full ring of integers $\mathcal{O}_K$ of $K$.
Bannai, Kenichi +2 more
core +1 more source
On the vanishing of cohomologies of $p$-adic Galois representations associated with elliptic curves
, 2014 Let $K$ be a $p$-adic field and $E$ an elliptic curve over $K$ with potential good reduction. For some large Galois extensions $L$ of $K$ containing all $p$-power roots of unity, we show the vanishing of certain Galois cohomology groups of $L$ with ...
Dimabayao, Jerome T.
core