8 citations · 46 across the 57 of their papers we have counts for
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Effective results on linear dependence for elliptic curves
Min Sha, Igor E. Shparlinski
Given a subgroup of rational points on an elliptic curve defined over of rank and any sufficiently large , assuming that the rank of is…
Counting and testing dominant polynomials
Artūras Dubickas, Min Sha
In this paper, we concentrate on counting and testing dominant polynomials with integer coefficients. A polynomial is called dominant if it has a simple root whose modulus is stric…
On the lattices from elliptic curves over finite fields
Min Sha
In this paper, we continue the recent work of Fukshansky and Maharaj on lattices from elliptic curves over finite fields. We show that there exist bases formed by minimal vectors f…
Lang-Trotter and Sato-Tate Distributions in Single and Double Parametric Families of Elliptic Curves
Min Sha, Igor E. Shparlinski
We obtain new results concerning Lang-Trotter conjecture on Frobenius traces and Frobenius fields over single and double parametric families of elliptic curves. We also obtain simi…
Counting degenerate polynomials of fixed degree and bounded height
Artūras Dubickas, Min Sha
In this paper, we give sharp upper and lower bounds for the number of degenerate monic (and arbitrary, not necessarily monic) polynomials with integer coefficients of fixed degree…
Explicit form of Cassels' -adic embedding theorem for number fields
Arturas Dubickas, Min Sha, Igor E. Shparlinski
In this paper, we mainly give a general explicit form of Cassels' -adic embedding theorem for number fields. We also give its refined form in the case of cyclotomic fields. As a…