Results 21 to 30 of about 667 (60)
, 2016 We revisit the mathematics that Ramanujan developed in connection with the famous "taxi-cab" number $1729$. A study of his writings reveals that he had been studying Euler's diophantine equation $$ a^3+b^3=c^3+d^3.
Ono, Ken, Trebat-Leder, Sarah
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Complete verification of strong BSD for many modular abelian surfaces over ${\mathbf {Q}}$
Forum of Mathematics, SigmaWe develop the theory and algorithms necessary to be able to verify the strong Birch–Swinnerton-Dyer Conjecture for absolutely simple modular abelian varieties over ${\mathbf {Q}}$ . We apply our methods to all 28 Atkin–Lehner quotients of $X_0(
Timo Keller, Michael Stoll
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Rational torsion points on abelian surfaces with quaternionic multiplication
Forum of Mathematics, SigmaLet A be an abelian surface over ${\mathbb {Q}}$ whose geometric endomorphism ring is a maximal order in a non-split quaternion algebra. Inspired by Mazur’s theorem for elliptic curves, we show that the torsion subgroup of $A({\mathbb {Q}})$
Jef Laga +3 more
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Rank jumps and multisections of elliptic fibrations on K3 surfaces
Forum of Mathematics, SigmaWe consider the countably many families $\mathcal {L}_d$ , $d\in \mathbb {N}_{\geq 2}$ , of K3 surfaces admitting an elliptic fibration with positive Mordell–Weil rank. We prove that the elliptic fibrations on the very general member of these
Alice Garbagnati, Cecília Salgado
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Genus-2 Jacobians with torsion points of large order
, 2014 We produce new explicit examples of genus-2 curves over the rational numbers whose Jacobian varieties have rational torsion points of large order. In particular, we produce a family of genus-2 curves over Q whose Jacobians have a rational point of order ...
Howe, Everett W.
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The Manin–Peyre conjecture for smooth spherical Fano varieties of semisimple rank one
Forum of Mathematics, SigmaThe Manin–Peyre conjecture is established for a class of smooth spherical Fano varieties of semisimple rank one. This includes all smooth spherical Fano threefolds of type T as well as some higher-dimensional smooth spherical Fano varieties.
Valentin Blomer +3 more
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On the factor alpha in Peyre's constant
, 2013 For an arbitrary del Pezzo surface S, we compute alpha(S), which is the volume of a certain polytope in the dual of the effective cone of S, using Magma and Polymake.
Derenthal, Ulrich +2 more
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On classification of groups of points on abelian varieties over finite fields [PDF]
, 2015 In this paper we improve our previous results on classification of groups of points on abelian varieties over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given $k$-isogeny class.Comment: 9 ...
Rybakov, Sergey
core
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
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Improvements on dimension growth results and effective Hilbert’s irreducibility theorem
Forum of Mathematics, SigmaWe sharpen and generalize the dimension growth bounds for the number of points of bounded height lying on an irreducible algebraic variety of degree d, over any global field.
Raf Cluckers +4 more
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