Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 6 of 6
Full-Text Articles in Number Theory
The Spectrum Of Nim-Values For Achievement Games For Generating Finite Groups, Bret J. Benesh, Dana C. Ernst, Nándor Sieben
The Spectrum Of Nim-Values For Achievement Games For Generating Finite Groups, Bret J. Benesh, Dana C. Ernst, Nándor Sieben
Mathematics Faculty Publications
We study an impartial achievement game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The game ends when the jointly selected elements generate the group. The last player able to make a move is the winner of the game. We prove that the spectrum of nim-values of these games is {0, 1, 2, 3, 4}. This positively answers two conjectures from a previous paper by the last two authors.
Provably Weak Instances Of Plwe Revisited, Again, Katherine Mendel
Provably Weak Instances Of Plwe Revisited, Again, Katherine Mendel
CSB and SJU Distinguished Thesis
Learning with Errors has emerged as a promising possibility for postquantum cryptography. Variants known as RLWE and PLWE have been shown to be more efficient, but the increased structure can leave them vulnerable to attacks for certain instantiations. This work aims to identify specific cases where proposed cryptographic schemes based on PLWE work particularly poorly under a specific attack.
Comparing Local Constants Of Ordinary Elliptic Curves In Dihedral Extensions, Sunil Chetty
Comparing Local Constants Of Ordinary Elliptic Curves In Dihedral Extensions, Sunil Chetty
Mathematics Faculty Publications
We establish, for a substantial class of elliptic curves, that the arithmetic local constants introduced by Mazur and Rubin agree with quotients of analytic root numbers.
On The Dimension Of Algebraic-Geometric Trace Codes, Phong Le, Sunil Chetty
On The Dimension Of Algebraic-Geometric Trace Codes, Phong Le, Sunil Chetty
Mathematics Faculty Publications
We study trace codes induced from codes defined by an algebraic curve X. We determine conditions on X which admit a formula for the dimension of such a trace code. Central to our work are several dimension reducing methods for the underlying functions spaces associated to X.
Arithmetic Local Constants For Abelian Varieties With Extra Endomorphisms, Sunil Chetty
Arithmetic Local Constants For Abelian Varieties With Extra Endomorphisms, Sunil Chetty
Mathematics Faculty Publications
This work generalizes the theory of arithmetic local constants, introduced by Mazur and Rubin, to better address abelian varieties with a larger endomorphism ring than ℤ. We then study the growth of the p∞- Selmer rank of our abelian variety, and we address the problem of extending the results of Mazur and Rubin to dihedral towers k ⊂ K ⊂ F in which [F : K] is not a p-power extension.
Computing Local Constants For Cm Elliptic Curves, Sunil Chetty, Lung Li
Computing Local Constants For Cm Elliptic Curves, Sunil Chetty, Lung Li
Mathematics Faculty Publications
Let E/k be an elliptic curve with CM by O. We determine a formula for (a generalization of) the arithmetic local constant of Mazur-Rubin at almost all primes of good reduction. We apply this formula to the CM curves defined over Q and are able to describe extensions F/Q over which the O-rank of E grows.