R. Andrew Ohana

Publications (2)0 Total impact

• Source

  Available from: ArXiv

  Article: A Database of Elliptic Curves over Q(sqrt(5)) - First Report

  Jonathan Bober, Alyson Deines, Ariah Klages-Mundt, Benjamin LeVeque, R. Andrew Ohana, Ashwath Rabindranath, Paul Sharaba, William Stein
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  ABSTRACT: We describe a tabulation of (conjecturally) modular elliptic curves over the field Q(sqrt(5)) up to the first curve of rank 2. Using an efficient implementation of an algorithm of Lassina Dembele, we computed tables of Hilbert modular forms of weight (2,2) over Q(sqrt(5)), and via a variety of methods we constructed corresponding elliptic curves, including (again, conjecturally) all elliptic curves over Q(sqrt(5)) that have conductor with norm less than or equal to 1831.
  02/2012;
• Source

  Available from: ArXiv

  Article: On well-rounded sublattices of the hexagonal lattice

  Lenny Fukshansky, Daniel Moore, R. Andrew Ohana, Whitney Zeldow
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  ABSTRACT: We produce an explicit parameterization of well-rounded sublattices of the hexagonal lattice in the plane, splitting them into similarity classes. We use this parameterization to study the number, the greatest minimal norm, and the highest signal-to-noise ratio of well-rounded sublattices of the hexagonal lattice of a fixed index. This investigation parallels earlier work by Bernstein, Sloane, and Wright where similar questions were addressed on the space of all sublattices of the hexagonal lattice. Our restriction is motivated by the importance of well-rounded lattices for discrete optimization problems. Finally, we also discuss the existence of a natural combinatorial structure on the set of similarity classes of well-rounded sublattices of the hexagonal lattice, induced by the action of a certain matrix monoid. Comment: 21 pages (minor correction to the proof of Lemma 2.1); to appear in Discrete Mathematics
  07/2010;