English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We provide an infinite sequence of upper bounds for the number of rational points of absolutely irreducible smooth projective curves X over a finite field, starting from Weil classical bound, continuing to Ihara bound, passing through infinitely many n-th order Weil bounds and ending asymptotically to Drinfeld-Vl˘ adut¸boundadut¸adut¸bound. We relate this set of bounds to Oesterle one, proving that these are inverse functions in some sense. We explain how Riemann hypothesis for the curve X can be merely seen as an euclidean property, coming from the Toeplitz shape of some intersection matrix on the surface X × X together with the general theory of symmetric Toeplitz matrices. We also give some interpretation for the defect of asymptotically exact towers. This is achieved by pushing further the classical Weil proof in term of eu-clidean relationships between classes in the euclidean part F X of the numerical group Num(X × X) generated by classes of graphs of iterations of the Frobenius morphism. The noteworthy Toeplitz shape of their intersection matrix takes a central place by implying a very strong cyclic structure on F X .

transactions of the american mathematical society

A unified viewpoint for upper bounds for the number of points of curves over finite fields via euclidean geometry and semi-definite symmetric Toeplitz matrices