Results 21 to 30 of about 140 (37)

The yoga of the Cassels-Tate pairing

, 2007
Cassels has described a pairing on the 2-Selmer group of an elliptic curve which shares some properties with the Cassels-Tate pairing.
Brown, Cassels, Cassels, Milne, Serre, Serre, Serre, Silverman   +7 more
core   +2 more sources

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, Bourgain, Burgess, Friedlander, Glyn Harman, Harman, Igor E. Shparlinski   +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, David, Chantal, Koukoulopoulos, Dimitris, Smith, Ethan   +3 more
core   +1 more source

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

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, Chandrasekharan, Everest, Frey, Katherine Stange, van der Poorten   +5 more
core   +1 more source

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, Coates, Cornut, Diem, Dokchitser, Dokchitser, Hachimori, Kolyvagin, Kramer, Milne, Nekovář, Nekovář, Rohrlich, Serre, Silverman, Tate, Tim Dokchitser, Vladimir Dokchitser   +17 more
core   +4 more sources

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, Ekedahl, Everest, Everest, Everest, Hall, Jr.,, Ingram, Katherine E. Stange, Lang, Schmidt, Silverman, Silverman, Silverman, Silverman, Sprindzuk, Stein, et. al.,   +15 more
core   +1 more source

$p$-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, Furusho, Hidekazu, Kobayashi, Shinichi   +2 more
core   +1 more source

Elliptic Reciprocity [PDF]

, 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, Bombardier, Kevin M., Cole, Matthew M., Morrell, Thomas A., Scott, Cory B.   +4 more
core  

On Kato's local epsilon-isomorphism Conjecture for rank one Iwasawa modules

, 2013
This paper contains a complete proof of Fukaya's and Kato's epsilon$-isomorphism conjecture in [23] for invertible \Lambda-modules (the case of V = V_0(r) where V_0 is unramified of dimension 1).
Berger, Bertrand, Bouganis, Breuning, Burns, Burns, Burns, Flach, Fukaya, Knudsen, Nekovář, Otmar Venjakob, Perrin-Riou, Tate, Yasuda   +14 more
core   +1 more source