We provide explicit formulae for realising the group law in Jacobians of superelliptic curves of genus 3 and C3,4 curves. It is shown that two distinct elements in the Jacobian of a C3,4 curve can be added with 150 multiplications and 2 inversions in the field of definition of the curve, while an element can be doubled with 174 multiplications and 2 inversions. In superelliptic curves, 10 multi...

Within uncertain technological progress, a firm has to decide when to update its technology and select a new one among a non-decreasing range over time. Under constant return to scale, the best existing technology is implemented. Replacement is triggered not only when the firm operated technology is sufficiently obsolete but also the wedge between the latest and the state of the arts grades is ...

In this paper, dependent and independent variable transformations are introduced to solve a generalized sinh–Gordon equation by using the binary F-expansion method and the knowledge of elliptic equation and Jacobian elliptic functions. Many different new exact solutions such as double periodic wave and complex wave solutions are obtained. Some previous results are extended. 2013 Elsevier Inc. A...

Let X be a nonsingular complex variety and D a reduced effective divisor in X. In this paper we study the conditions under which the formula cSM (1U ) = c(DerX(− logD)) ∩ [X] is true. We prove that this formula is equivalent to a RiemannRoch type of formula. As a corollary, we show that over a surface, the formula is true if and only if the Milnor number equals the Tjurina number at each singul...

We summarise recent advances in techniques for solving Diophantine problems on hyperelliptic curves; in particular, those for finding the rank of the Jacobian, and the set of rational points on the curve.

Representations of the wavefunction of the multiparticle Schrödinger equation using an unconstrained sum of Slater determinants have the potential to be very efficient, except that they cannot capture the interelectron cusp. To remedy this shortcoming, we extend these representations to include interelectron geminals and analyze the algorithmic implications of doing so.

Using the p-adic uniformization of Shimura varieties we determine, for some of them, over which local fields they have rational points. Using this we show in some new curve cases that the jacobians are even in the sense of [PS].

We prove that there are exactly 149 genus two curves C defined over Q such that there exists a nonconstant morphism π : X1(N)→ C defined over Q and the jacobian of C is Q-isogenous to the abelian variety Af attached by Shimura to a newform f ∈ S2(Γ1(N)). We determine the corresponding newforms and present equations for all these curves.

Introduction and Review 2 1. Period domains and monodromy 4 2. Elliptic curves 8 3. Period mappings: an example 12 3.1. Asymptotics of the period map 14 4. Hodge structures of weight one 15 5. Hodge structures of weight two 18 6. Poincaré residues 20 7. Properties of the period mapping 24 8. The Jacobian ideal and the local Torelli theorem 25 9. The Horizontal Distribution Distance Decreasing P...