4 citations · 12 across the 12 of their papers we have counts for
14 papers
On the Geometry and Shapes of Rank 2 Log Unit Lattices
Jose Cruz, Erik Holmes, Fatemeh Jalalvand +3
Every number field canonically gives rise to two lattices: its ring of integers and its log unit lattice. While the shapes of the former have undergone extensive research, far less…
Principal Well-Rounded Ideals of real quadratic fields
Morgan Smith, Ha T. N. Tran
It has been well known since Gauss that the principality of an ideal in a real quadratic field is equivalent to the solvability of a certain generalized Pell equations. In this…
Well-Rounded Twists of the Ring of Integers in Cyclic Cubic Fields
Nam H. Le, Dat T. Tran, David Karpuk +1
Computing well-rounded twists of ideals in number fields has been done when the field degree is . In this paper, we develop a new algorithm to detect whether a basis of an ideal…
Gross lattices of supersingular elliptic curves
Chenfeng He, Gaurish Korpal, Ha T. N. Tran +1
Let be a prime, be a supersingular elliptic curve defined over , and be its (geometric) endomorphism ring. Earlier results of Chevyrev-Gal…
Well-Rounded ideal lattices of cyclic cubic and quartic fields
Dat T. Tran, Nam H. Le, Ha T. N. Tran
In this paper, we find criteria for when cyclic cubic and cyclic quartic fields have well-rounded ideal lattices. We show that every cyclic cubic field has at least one well-rounde…
The size function for imaginary cyclic sextic fields
Ha Thanh Nguyen Tran, Peng Tian, Amy Feaver
In this paper, we investigate the size function for number fields. This size function is analogous to the dimension of the Riemann-Roch spaces of divisors on an algebraic cur…
Well-Rounded Twists of Ideal Lattices from Imaginary Quadratic Fields
Nam H. Le, Dat T. Tran, Ha T. N. Tran
In this paper, we investigate the properties of well-rounded twists of a given ideal lattice of an imaginary quadratic field . We show that every ideal lattice of has at…
Reduced ideals from the reduction algorithm
Ha Thanh Nguyen Tran
The reduction algorithm is used to compute reduced ideals of a number field. However, there are reduced ideals that can never be obtained from this algorithm. In this paper, we wil…
Well-Rounded Lattices for Coset Coding in MIMO Wiretap Channels
Oliver W. Gnilke, Amaro Barreal, Alex Karrila +3
The concept of well-rounded lattices has recently found important applications in the setting of a fading single-input single-output (SISO) wiretap channel. It has been shown that,…
The size function for cyclic cubic fields
Ha Thanh Nguyen Tran, Peng Tian
The size function for a number field is an analogue of the dimension of the Riemann-Roch spaces of divisors on an algebraic curve. It was conjectured to attain its maximum at the t…
Well-Rounded Lattices for Reliability and Security in Rayleigh Fading SISO Channels
Oliver Wilhelm Gnilke, Ha Thanh Nguyen Tran, Alex Karrila +1
For many wiretap channel models asymptotically optimal coding schemes are known, but less effort has been put into actual realizations of wiretap codes for practical parameters. Bo…
Computing dimensions of spaces of Arakelov divisors of number fields
Ha Thanh Nguyen Tran
The function for a number field is analogous to the dimension of the Riemann-Roch spaces at divisors on an algebraic curve. We provide a method to compute this function for n…
A generalization of reduced Arakelov divisors of a number field
Ha Thanh Nguyen Tran
Let . Inspired by the LLL-algorithm, we define strongly -reduced divisors of a number field which are generalized from the concept of reduced Arakelov divisors. Mo…
On reduced Arakelov divisors of real quadratic fields
Ha Thanh Nguyen Tran
We generalize the concept of reduced Arakelov divisors and define -reduced divisors for a given number . These -reduced divisors have remarkable properties which ar…