Results 21 to 30 of about 278 (30)
Rational points on Erdős–Selfridge superelliptic curves [PDF]
, 2015 Given k⩾2k⩾2, we show that there are at most finitely many rational numbers xx and y≠0y≠0 and integers ℓ⩾2ℓ⩾2 (with (k,ℓ)≠(2,2)(k,ℓ)≠(2,2)) for which $$\begin{eqnarray}x(x+1)\cdots (x+k-1)=y^{\ell }.\end{eqnarray}$$ In particular, if we assume that ℓℓ is
Darmon +6 more
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Root numbers of elliptic curves in residue characteristic 2
, 2006 To determine the global root number of an elliptic curve defined over a number field, one needs to understand all the local root numbers. These have been classified except at places above 2, and in this paper we attempt to complete the classification. At
Dokchitser, T., Dokchitser, V.
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Dihedral Group, 4-Torsion on an Elliptic Curve, and a Peculiar Eigenform Modulo 4
, 2018 We work out a non-trivial example of lifting a so-called weak eigenform to a true, characteristic 0 eigenform. The weak eigenform is closely related to Ramanujan's tau function whereas the characteristic 0 eigenform is attached to an elliptic curve ...
Kiming, Ian, Rustom, Nadim
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On distribution formulas for complex and $\ell$-adic polylogarithms
, 2020 We study an $\ell$-adic Galois analogue of the distribution formulas for polylogarithms with special emphasis on path dependency and arithmetic behaviors.
H Gangl +6 more
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A note on Fontaine theory using different Lubin-Tate groups
, 2013 Using different Lubin-Tate groups, we compare $(\phi, \Gamma)$ modules associated to a Galois representation via Fontaine's ...
Chiarellotto, Bruno R. +1 more
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Elliptic curves with maximal Galois action on their torsion points
, 2008 Given an elliptic curve E over a number field k, the Galois action on the torsion points of E induces a Galois representation, \rho_E : Gal(\bar{k}/k) \to GL_2(\hat{Z}).
Zywina, David
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Abelian varieties over large algebraic fields with infinite torsion [PDF]
, 2010 Let A be an abelian variety of positive dimension defined over a number field K and let Kbar be a fixed algebraic closure of K. For each element sigma of the absolute Galois group Gal(Kbar/K), let Kbar(sigma) be the fixed field of sigma in Kbar. We shall
Zywina, David
core
Filtrations of dc-weak eigenforms
, 2017 The notions of strong, weak and dc-weak eigenforms mod $p^n$ was introduced and studied by Chen, Kiming and Wiese. In this work, we prove that there can be no uniform weight bound (that is, depending only on $p$, $n$) on dc-weak eigenforms mod $p^n$ of ...
Rustom, Nadim
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Fontaine-Laffaille modules and strongly divisible modules
, 2019 In this note, we study the relation between Fontaine-Laffaille modules and strongly divisible modules, without assuming the main theorem of Fontaine-Laffaille (but we need to assume the main results concerning strongly divisible modules).
Gao, Hui
core
Recovering modular forms and representations from tensor and symmetric powers
, 2004 We consider the problem of determining the relationship between two representations knowing that some tensor or symmetric power of the original represetations coincide.
Rajan, C. S.
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