16,282 research outputs found
The Hasse Norm Principle For Biquadratic Extensions
We give an asymptotic formula for the number of biquadratic extensions of the
rationals of bounded discriminant that fail the Hasse norm principle.Comment: 19 pages. Proof of Theorem 1 improved/simplified. Accepted by Journal
de Th\'eorie des Nombres de Bordeau
Give Up the Ghost Hunt: A Defense of Limited Scope Representation and Ghostwriting in Rhode Island
A Positive Proportion of Hasse Principle Failures in a Family of Ch\^atelet Surfaces
We investigate the family of surfaces defined by the affine equation where and develop an
asymptotic formula for the frequency of Hasse principle failures. We show that
a positive proportion (roughly 23.7%) of such surfaces fail the Hasse
principle, by building on previous work of la Bret\`{e}che and Browning.Comment: 13 pages, comments welcome. To appear in International Journal of
Number Theor
Evidence that an RGD-dependent receptor mediates the binding of oligodendrocytes to a novel ligand in a glial-derived matrix.
A simple adhesion assay was used to measure the interaction between rat oligodendrocytes and various substrata, including a matrix secreted by glial cells. Oligodendrocytes bound to surfaces coated with fibronectin, vitronectin and a protein component of the glial matrix. The binding of cells to all of these substrates was inhibited by a synthetic peptide (GRGDSP) modeled after the cell-binding domain of fibronectin. The component of the glial matrix responsible for the oligodendrocyte interaction is a protein which is either secreted by the glial cells or removed from serum by products of these cultures; serum alone does not promote adhesion to the same extent as the glial-derived matrix. The interaction of cells with this glial-derived matrix requires divalent cations and is not mediated by several known RGD-containing extracellular proteins, including fibronectin, vitronectin, thrombospondin, type I and type IV collagen, and tenascin
Average Bateman--Horn for Kummer polynomials
For any and almost all smaller than
, we show that the polynomial takes the expected number
of prime values as ranges from 1 to . As a consequence, we deduce
statements concerning variants of the Hasse principle and of the integral Hasse
principle for certain open varieties defined by equations of the form
where is a
quadratic extension. A key ingredient in our proof is a new large sieve
inequality for Dirichlet characters of exact order .Comment: V2: Minor correction
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