Browsing by Author "Wijesiri G S"

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Codes over rings of size p2 and lattices over imaginary quadratic fields
(Finite Fields Appl., 2010) Shaska T; Shore C; Wijesiri G S
Let ?>0 be a square-free integer congruent to 3 mod 4 and OK the ring of integers of the imaginary quadratic field View the MathML source. Codes C over rings OK/pOK determine lattices ??(C) over K . If p?? then the ring R:=OK/pOK is isomorphic to Fp2 or Fp?Fp. Given a code C over R, theta functions on the corresponding lattices are defined. These theta series ???(C)(q) can be written in terms of the complete weight enumerators of C . We show that for any two ?
Degree 4 coverings of elliptic curves by genus 2
(Albanian J. Math., 2008) Shaska T; Wijesiri G S; Wolf S; Woodland L
Genus two curves covering elliptic curves have been the object of study of many articles. For a ?xed degree n the subloci of the moduli space M_2 of curves having a degree n elliptic subcover has been computed for n=3,5 and discussed in detail for n odd; see [17, 22, 3, 4]. When the degree of the cover is even the case in general has been treated in [16]. In this paper we compute the sublocus of M_2 of curves having a degree 4 elliptic subcover.
Theta nulls of cyclic curves of small genus
(Albanian J. Math., 2007) Previato E; Shaska T; Wijesiri G S
We study relations among the classical thetanulls of cyclic curves, namely curves X (of genus g(X)>1) with an automorphism ? such that ? generates a normal subgroup of the group G of automorphisms, and g(X???? )=0 .0. Relations between thetanulls and branch points of the projection are the object of much classical work, especially for hyperelliptic curves, and of recent work, in the cyclic case. We determine the curves of genus 2 and 3 in the locus Mg(G,C) for all G that have a normal subgroup ??? as above, and all possible signatures C, via relations among their thetanulls.
Thetanulls of cyclic curves of genus 4
(Annual research symposium, FGS, University of Kelaniya, Kelaniya, 2013) Wijesiri G S
Let ? be an irreducible smooth projective curve of genus g>1 defined over the complex field C. When the curve is hyperelliptic, the curve has extra automorphism ? and has an equation y^2=f(x), where x is an affine coordinate on P^1 and ? has order 2. By Hurwitz formula, there are 2g+2 branch points p_1,?,p_(2g+2) in P^1 where P^1 denotes the projective line. The problem of expressing branch points in terms of transcendentals (period matrix, thetanulls, etc.,) is an old problem that goes back to Riemann, Jacobi, Picard and Rosenhein. In our previous work [1] we give treatment for the problem of hyperelliptic curves of genus 2 and 3. For genus 2 curves there are 16 thetanulls. In [1] we express the branch points of hyperelliptic curves in terms of the even theta constants and also some relations among even theta constants. Inverting such period map has an application in fast genus 2 curves arithmetic in cryptography. According to Gaudry [2], the cost of scalar multiplication of elliptic curves is twice large as for genus 2 curves and genus 2 cryptosystem is faster than an elliptic curve cryptosystem. Author of [2] uses formulae for the arithmetic in the Kummer surface that comes from the theory of Theta functions. In [1], authors provide formulae that can be used in cryptosystem of genus 2 and genus 3 algebraic curves. In this paper we determine the hyperelliptic curves of genus 4 in terms of thetanulls and further study relations among the classical thetanulls of such curves ?. In our work we use formulas for small genus curves introduced by Rosenhein, Thomae?s formulas for hyperelliptic curves, some recent results of Hurwitz space theory, and symbolic manipulation.