0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 1. Multiple groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 2. K-groups and transfer factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 3. ...

We give a mathematical interpretation in terms of algebraic tori of Lucas-based cryptosystems, XTR, and the conjectural generalizations in [2]. We show that the varieties underlying these systems are quotients of algebraic tori by actions of products of symmetric groups. Further, we use these varieties to disprove conjectures from [2].

We give a direct construction of specific central idempotent in the endomorphism algebra finite lattice T. This is associated with all possible sublattices T which are totally ordered. A generalization considered conjectural fashion and proved experimentally to hold many cases.

Abstract We prove the existence of quasi-Jacobi form solutions for an analogue Kaneko–Zagier differential equation Jacobi forms. The transformation properties under group are derived. A special feature is polynomial dependence index parameter. results yield explicit conjectural description all double ramification cycle integrals in Gromov–Witten theory K3 surfaces.

The aim of this paper is to show how a conjectural lower bound on the canonical height function in spirit Lang and Silverman leads an explicit uniform number rational points curves genus $g\geq 2$ over field.

We prove the conjectural relation between the Stokes matrix for the quantum cohomology of X and an exceptional collection generating D bcoh(X) when X is a smooth cubic surface. The proof is based on a toric degeneration of a cubic surface, the Givental’s mirror theorem for toric manifolds, and the Picard-Lefschetz theory.