Results 11 to 20 of about 140 (37)
Non‐vanishing theorems for central L‐values of some elliptic curves with complex multiplication
Proceedings of the London Mathematical Society, Volume 121, Issue 6, Page 1531-1578, December 2020., 2020 Abstract The paper uses Iwasawa theory at the prime p=2 to prove non‐vanishing theorems for the value at s=1 of the complex L‐series of certain quadratic twists of the Gross family of elliptic curves with complex multiplication by the field K=Q(−q), where q is any prime ≡7mod8.
John Coates, Yongxiong Li
wiley +1 more source
L‐equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces
Bulletin of the London Mathematical Society, Volume 52, Issue 2, Page 395-409, April 2020., 2020 Abstract We construct non‐trivial L‐equivalence between curves of genus one and degree five, and between elliptic surfaces of multisection index five. These results give the first examples of L‐equivalence for curves (necessarily over non‐algebraically closed fields) and provide a new bit of evidence for the conjectural relationship between L ...
Evgeny Shinder, Ziyu Zhang
wiley +1 more source
Transactions of the London Mathematical Society, Volume 6, Issue 1, Page 22-52, December 2019., 2019 Abstract Recently, there has been much interest in studying the torsion subgroups of elliptic curves base‐extended to infinite extensions of Q. In this paper, given a finite group G, we study what happens with the torsion of an elliptic curve E over Q when changing base to the compositum of all number fields with Galois group G.
Harris B. Daniels +2 more
wiley +1 more source
On the class numbers of certain number fields obtained from points on elliptic curves II [PDF]
, 2008 Let k be a number field of finite degree and k an algebraic closure of k, and let E/k be an elliptic curve which is given by the Weierstrass equation of the form y2 = f(x), where f(x) 2 k[x] is a cubic polynomial. For a subset Ξ of P1(k) (regarded as k [
Sato, Atsushi
core +3 more sources
Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average
, 2007 We prove that the set of Farey fractions of order $T$, that is, the set $\{\alpha/\beta \in \Q : \gcd(\alpha, \beta) = 1, 1 \le \alpha, \beta \le T\}$, is uniformly distributed in residue classes modulo a prime $p$ provided $T \ge p^{1/2 +\eps}$ for any ...
Cojocaru, A. C., Shparlinski, I. E.
core +1 more source
A remark on Tate's algorithm and Kodaira types
, 2013 We remark that Tate's algorithm to determine the minimal model of an elliptic curve can be stated in a way that characterises Kodaira types from the minimum of v(a_i)/i.
Dokchitser, Tim, Dokchitser, Vladimir
core +1 more source
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
core +2 more sources
Average Analytic Ranks of Elliptic Curves over Number Fields
Forum of Mathematics, SigmaWe give a conditional bound for the average analytic rank of elliptic curves over an arbitrary number field. In particular, under the assumptions that all elliptic curves over a number field K are modular and have L-functions which satisfy the ...
Tristan Phillips
doaj +1 more source
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.
core +3 more sources
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