Results 1 to 9 of about 12 (9)
Karpatsʹkì Matematičnì Publìkacìï, 2013 A proof of nondegeneracy of the Tate pairing and Kolyvagin's formula for elliptic curves with good reductions over an $n$-dimensional $(n\leq 3)$ pseudolocal field, the Tate pairing associated to an isogeny between abelian varieties over pseudolocal ...
V.I. Nesteruk
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On the Kolyvagin formula for elliptic curves with good reductions over pseudolocal fields [PDF]
Математичні Студії, 2013 We consider the {relationships between the} local Artin map$heta colon K^* o mathrm{Gal}(K^{ab}/K)$ {and the} Hilbert symbol $(cdot,,cdot)colon K^*/K^{*m} imes K^*/K^{*m} longrightarrow mu_m$ for {a} general local field, as well as {between} the Tate ...
V. I. Nesteruk
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Refined class number formulas and Kolyvagin systems [PDF]
Compositio Mathematica, 2010 Abstract We use the theory of Kolyvagin systems to prove (most of) a refined class number formula conjectured by Darmon. We show that, for every odd prime p , each side of Darmon’s conjectured formula (indexed by positive integers n ...
Mazur, Barry, Rubin, Karl
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Heegner points in Coleman families
Proceedings of the London Mathematical Society, Volume 122, Issue 1, Page 124-152, January 2021., 2021 Abstract We construct two‐parameter analytic families of Galois cohomology classes interpolating the étale Abel–Jacobi images of generalised Heegner cycles, with both the modular form and Grössencharacter varying in p‐adic families.
Dimitar Jetchev +2 more
wiley +1 more source
, 2023 Let $p$ be a prime and $\mathcal{K}$ be an imaginary quadratic field. In this paper we generalize a recent construction of a new type of $p$-adic $L$-function and $p$-adic Waldspurger formula by Andreatta-Iovita for $p$ non-split in $\mathcal{K}$, as long as the $\mathrm{GL}_2$ automorphic representation is principal series at $p$.
Fan, Yangyu, Wan, Xin
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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
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On the Birch–Swinnerton‐Dyer conjecture and Schur indices
Bulletin of the London Mathematical Society, Volume 50, Issue 6, Page 1027-1034, December 2018., 2018 Abstract For every odd prime p, we exhibit families of irreducible Artin representations τ with the property that for every elliptic curve E the order of the zero of the twisted L‐function L(E,τ,s) at s=1 must be a multiple of p. Analogously, the multiplicity of τ in the Selmer group of E must also be divisible by p.
Matthew Bisatt, Vladimir Dokchitser
wiley +1 more source
Journal of Numbers, Volume 2014, Issue 1, 2014., 2014 We consider certain quartic twists of an elliptic curve. We establish the rank of these curves under the Birch and Swinnerton‐Dyer conjecture and obtain bounds on the size of Shafarevich‐Tate group of these curves. We also establish a reduction between the problem of factoring integers of a certain form and the problem of computing rational points on ...
Iftikhar A. Burhanuddin +2 more
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An Algorithm for Computing the Singularities of the Plane Model of X0(N)
AxiomsLet ΦN(X,Y) be the N-th classical modular polynomial and let Z0(N)={(X,Y)∈C2∣ΦN(X,Y)=0} be the plane model of the modular curve X0(N). We present an explicit procedure that, for a prime ℓ, enumerates all non-cuspidal singular points of Z0(ℓ) over C and ...
Sanmin Wang, Haodong Xu
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