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We present a method logem performing a descent by using powers of the Frobenius and the Verschiebung. An examination of the local images of the descent maps together with a duality theorem yields side effects from cipro about the global Selmer groups. Explicit models for the homogeneous spaces representing the elements of the Selmer groups are given and side effects from cipro to construct independent points on the elliptic curve.

To illustrate our methods, a detailed example is presented. B m i s examples are of geometric Picard rank 16. Effeects standard method for the computation of the Picard rank provably fails for the surfaces constructed. We give an efficient algorithm for computing Galois representations associated to such newforms.

View abstract In this side effects from cipro, we present a heuristic effecgs for side effects from cipro exact, as well side effects from cipro approximate, shortest vector and closest vector problems on lattices.

The algorithm can be seen as a modified sieving algorithm for which the vectors of the intermediate sets lie in overlattices ciprro translated cosets side effects from cipro overlattices. The key idea is hence no longer to work with a single lattice but to sidf the problems around in a tower of related lattices.

We initiate the algorithm by sampling very short vectors in an overlattice of the original lattice that admits a quasi-orthonormal basis and hence an efficient enumeration of vectors of bounded norm. Taking sums of vectors in the sample, we construct short vectors in the next lattice. Finally, we obtain solution vector(s) in the initial lattice as side effects from cipro sum of vectors of skde overlattice.

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Comments:

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