7 citations · 16 across the 7 of their papers we have counts for
9 papers
Intractability of Learning the Discrete Logarithm with Gradient-Based Methods
Rustem Takhanov, Maxat Tezekbayev, Artur Pak +3
The discrete logarithm problem is a fundamental challenge in number theory with significant implications for cryptographic protocols. In this paper, we investigate the limitations…
Classification of Frobenius Forms in five variables
Zhibek Kadyrsizova, Janet Page, Jyoti Singh +3
We classify Frobenius forms, a special class of homogeneous polynomials in characteristic , in up to five variables over an algebraically closed field. We also point out some…
Lower Bounds on the F-pure Threshold and Extremal Singularities
Zhibek Kadyrsizova, Jennifer Kenkel, Janet Page +4
We prove that if is a reduced homogenous polynomial of degree , then its -pure threshold at the unique homogeneous maximal ideal is at least . We show, fur…
Cubic Surfaces of Characteristic Two
Zhibek Kadyrsizova, Jennifer Kenkel, Janet Page +4
Cubic surfaces in characteristic two are investigated from the point of view of prime characteristic commutative algebra. In particular, we prove that, the non-Frobenius split cubi…
Algebraic sets defined by the commutator matrix
Zhibek Kadyrsizova, Madi Yerlanov
In this paper we study algebraic sets of pairs of matrices defined by the vanishing of either the diagonal of their commutator matrix or its anti-diagonal. We find a system of para…
The variety defined by the matrix of diagonals is -pure
Zhibek Kadyrsizova
We prove that the variety defined by the determinant of the matrix of diagonals is -pure for matrices of all sizes and in all positive prime characteristics. Moreover, we find a…
The TestIdeals package for Macaulay2
Alberto F. Boix, Daniel J. Hernández, Zhibek Kadyrsizova +7
This note describes a \emph{Macaulay2} package for computations in prime characteristic commutative algebra. This includes Frobenius powers and roots, -linear and -l…
Nearly Commuting Matrices
Zhibek Kadyrsizova
We prove that the algebraic set of pairs of matrices with a diagonal commutator over a field of positive prime characteristic, its irreducible components, and their intersection ar…
On the behavior of singularities at the -pure threshold
Eric Canton, Daniel Hernández, Karl Schwede +6
We provide a family of examples where the -pure threshold and the log canonical threshold of a polynomial are different, but where does not divide the denominator of the …