Results 21 to 30 of about 161 (55)
The remaining cases of the Kramer-Tunnell conjecture
, 2016 For an elliptic curve $E$ over a local field $K$ and a separable quadratic extension of $K$, motivated by connections to the Birch and Swinnerton-Dyer conjecture, Kramer and Tunnell have conjectured a formula for computing the local root number of the ...
Cesnavicius, Kestutis, Imai, Naoki
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Tate-Shafarevich Groups and Frobenius Fields of Reductions of Elliptic Curves [PDF]
, 2007 Let $\E/\Q$ be a fixed elliptic curve over $\Q$ which does not have complex multiplication. Assuming the Generalized Riemann Hypothesis, A. C. Cojocaru and W.
Shparlinski, Igor E.
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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
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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
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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
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, 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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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
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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
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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
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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.
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