We show how the prescription of taking the absolute value of the fermion determinant in the integration measure of QCD at finite density, forgetting its phase, reproduces the correct thermodynamical limit. This prescription, which applies also to other gauge theories with non-positive-definite integration measure, also has the advantage of killing finite size effects due to extremely small mean...

In this paper, we introduce the Fractional Window-w Multibase NonAdjacent Form (Frac-wmbNAF) method to perform the scalar multiplication. This method generalizes the recently developed Window-w mbNAF (wmbNAF) method by allowing an unrestricted number of precomputed points. We then make a comprehensive analysis of the most recent and relevant methods existent in the literature for the ECC scalar...

We construct Weil numbers corresponding to genus-2 curves with p-rank 1 over the finite field Fp2 of p 2 elements. The corresponding curves can be constructed using explicit CM constructions. In one of our algorithms, the group of Fp2 -valued points of the Jacobian has prime order, while another allows for a prescribed embedding degree with respect to a subgroup of prescribed order. The curves ...

In this paper, we construct a point on the Jacobian of a non-hyperelliptic genus four curve which is defined over a quadratic extension of the base field. We then show that this point generates the Mordell–Weil group of the Jacobian of the universal genus four curve.

We present a new technique to study Jacobian variety decompositions using subgroups of the automorphism group of the curve and the corresponding intermediate covers. In particular, this new method allows us to produce many new examples of genera for which there is a curve with completely decomposable Jacobian. These examples greatly extend the list given by Ekedahl and Serre of genera containin...

We give a new proof of Shiota’s theorem on Novikov’s conjecture, which states that the K.P. equation characterizes Jacobians among all indecomposable principally polarized abelian varieties. Mathematics Subject Classifications (1991): 14K25, 14H40.

We study the set of isomorphism classes of principal polarizations on abelian varieties of GL2-type. As applications of our results, we construct examples of curves C, C ′/Q of genus two which are nonisomorphic over Q̄ and share isomorphic unpolarized modular Jacobian varieties over Q; we also show a method to obtain genus two curves over Q whose Jacobian varieties are isomorphic to Weil’s restr...

where u : R × R → R is a vector of conserved variables (or state variables). For fluid dynamics, u is the vector of mass, momentum and energy denisties so that ∫ b a uj(x, t) dx is the total quantity of the j state variable in the interval at time t. Because these variables are conserved, ∫∞ −∞ uj(x, t) dx should be constant in t. The function f : R m → R is the flux function, which gives the r...

1. Complex multiplication. We say an abelian variety A of dimension g over a field K admits sufficiently many Complex Multiplications (smCM) if D = End(A) contains a commutative semi-simple algebra Λ ⊂ D of rank dimQ(Λ) = [Λ : Q] = 2g. In this case we say A is a CM abelian variety. A point z ∈ Ag(k) is called a CM point if z is the moduli point of a polarized abelian variety z = [(A,μ)] such th...