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Abstract: We show that many existing divisibility sequences can be seen as sequences of determinants of matrix divisibility sequences, which arise naturally as Jacobian matrices associated to groups o...
Squares in Polynomial Product Sequences
Squarefull numbers Polynomial Product Sequences Number Theory
2011/8/31
Abstract: Let F(n) be a polynomial of degree at least 2 with integer coefficients. We consider the products N_x=\prod_{1 \le n \le x} F(n) and show that N_x should only rarely be a perfect power. In p...
Given a graded sequence of ideals (a_m) on a smooth variety X, suppose that for every m we have a divisor E_m over X that computes the log canonical threshold of a_m, and such that the log discrepanc...
Valuations and asymptotic invariants for sequences of ideals
asymptotic invariants sequences
2010/11/22
We study asymptotic jumping numbers for graded sequences of ideals, and show that every such invariant is computed by a suitable real valuation of the function field. We conjecture that every valuati...
Power multiples in binary recurrence sequences: an approach by congruences
Power multiples binary recurrence sequences approach by congruences
2010/12/13
We introduce an elementary congruence-based procedure to look for q-th power multiples in arbitrary binary recurrence sequences (q 3). The procedure allows to prove that no such multiples exist in m...
Primitive Divisors of Certain Elliptic Divisibility Sequences
Elliptic curve Elliptic divisibility sequence Primitive diviso Canonical height
2010/11/30
We establish conditions necessary for the n-th element of any elliptic divisibility sequence generated by points on Ea : y2 = x3+ax to not have a primitive divisor. As a consequence of this, along wit...