منابع مشابه
High Rank Elliptic Curves with Torsion Z/2z× Z/4z Induced by Diophantine Triples
We construct an elliptic curve over the eld of rational functions with torsion group Z/2Z × Z/4Z and rank equal to 4, and an elliptic curve over Q with the same torsion group and rank 9. Both results improve previous records for ranks of curves of this torsion group. They are obtained by considering elliptic curves induced by Diophantine triples.
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Let k be an algebraically closed field of characteristic 2. We prove that the restricted nilpotent commuting variety C, that is the set of pairs of (n× n)-matrices (A,B) such that A2 = B2 = [A,B] = 0, is equidimensional. C can be identified with the ‘variety of n-dimensional modules’ for Z/2Z×Z/2Z, or equivalently, for k[X,Y ]/(X2, Y 2). On the other hand, we provide an example showing that the...
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Let a, a1, . . . , ad be positive integers, m1, . . . ,md nonnegative integers, and z1, . . . , zd complex numbers. We study expressions of the form ∑
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Using a recent improvement by Bettin and Chandee to a bound of Duke, Friedlander and Iwaniec (1997) on double exponential sums with Kloosterman fractions, we establish a uniformity of distribution result for the fractional parts of Dedekind sums s(m,n) with m and n running over rather general sets. Our result extends earlier work of Myerson (1988) and Vardi (1987). Using different techniques, w...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2015
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042115500748