A superspecial curve in characteristic p is a curve whose Jacobian is a product of supersingular elliptic curves. Using Igusa's result that h p (λ) has only simple roots, one can calculate how many supersingular elliptic curves have each possible automorphism group. Relying on Igusa's enumeration of all automorphism groups of genus 2 curves and Hashimoto… (More)
De Launey has conjectured and proved that for every prime p there exists a circulant generalized Hadamard matrix of order p 2 over the group Z p. We offer a new construction, generalize it, and prove that it is not isomorphic to the previous one for p ≥ 5. First let us recall some definitions and results from . Let H and G be finite multiplicative groups… (More)
We give some very interesting matrices which are orthogonal over groups and, as far as we know, referenced, but in fact undocumented. This note is not intended to be published but available for archival reasons.
On average, there are q r + o(q r=2) F q r-rational points on curves of genus g deened over F q r. This is also true if we restrict our average to genus g curves deened over Fq, provided r is odd or r > 2g. However, if r = 2;4; 6;: : : or 2g then the average is q r + q r=2 + o(q r=2). We give a number of proofs of the existence of these q r=2 \extra"… (More)
In pointwise differential geometry, i.e., linear algebra, we prove two theorems about the curvature operator of isomet-rically immersed submanifolds. We restrict our attention to Euclidean immersions because here the results are most easily stated and the curvature operator can be simply expressed as the sum of wedges of second fundamental form matrices.… (More)