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Using the "simplest cubic fields" of D. Shanks, we give a modified proof and an extension of a result of Uchida, showing how to obtain cyclic cubic fields with class number divisible by n, for any n.â€¦ (More)

- James S. Kraft, Lawrence C. Washington
- Math. Comput.
- 2007

Let K = Q( âˆš âˆ’d) be an imaginary quadratic field and let Q( âˆš 3d) be the associated real quadratic field. Starting from the Cohen-Lenstra heuristics and Scholzâ€™s theorem, we make predictions for theâ€¦ (More)

- Tsz-Wo Sze, Lawrence C. Washington
- Math. Comput.
- 2011

We present a novel idea to compute square roots over finite fields, without being given any quadratic nonresidue, and without assuming any unproven hypothesis. The algorithm is deterministic and theâ€¦ (More)

We study a family of quintic polynomials discoverd by Emma Lehmer. We show that the roots are fundamental units for the corresponding quintic fields. These fields have large class numbers and severalâ€¦ (More)

- Lawrence C. Washington
- SIGACT News
- 2008

1 Overview Elliptic curve cryptography was introduced in the mid 1980s and is now finding applicability in many public key situations. In particular, it provides a level of security comparable toâ€¦ (More)

- Daniel C. Shanks, Patrick J. Sime, Lawrence C. Washington
- Math. Comput.
- 1999

We study the imaginary quadratic fields such that the Iwasawa Î»2-invariant equals 1, obtaining information on zeros of 2-adic L-functions and relating this to congruences for fundamental units andâ€¦ (More)

- Paola Lanza, Lawrence C. Washington, M. Zanetti
- Viral immunology
- 1992

The study presents a new in vitro method to investigate the interaction between the glycoprotein (gp)120 of human immunodeficiency virus (HIV) and its receptor, CD4. The method is based on theâ€¦ (More)

- Lawrence C. Washington, i-Ã±a, Lawrence C. Washington
- 2010

Cohen and Lenstra have given a heuristic model which predicts the fraction of imaginary quadratic fields with class number divisible by a given odd prime p and of those whose class groups have aâ€¦ (More)

Let F0 = Q(âˆš âˆ’d) be an imaginary quadratic field with 3 âˆ¤ d and let K0 = Q(âˆš 3d). Let Îµ0 be the fundamental unit of K0 and let Î» be the Iwasawa Î»-invariant for the cyclotomic Z3-extension of F0. Theâ€¦ (More)

- Chatchawan Panraksa, Lawrence C. Washington
- Periodica Mathematica Hungarica
- 2017