Statistics for biquadratic covers of the projective line over finite fields

Homology of Projective Space over Finite Fields

Computing in Picard groups of projective curves over finite fields

We give algorithms for computing with divisors on projective curves over finite fields, and with their Jacobians, using the algorithmic representation of projective curves developed by Khuri-Makdisi. We show that various desirable operations can be performed efficiently in this setting: decomposing divisors into prime divisors; computing pull-backs and push-forwards of divisors under finite mor...

Extending Self-maps to Projective Space over Finite Fields

Using the closed point sieve, we extend to finite fields the following theorem proved by A. Bhatnagar and L. Szpiro over infinite fields: if X is a closed subscheme of P over a field, and φ : X → X satisfies φOX(1) ' OX(d) for some d ≥ 2, then there exists r ≥ 1 such that φ extends to a morphism P → P.

Classical Wavelet Transforms over Finite Fields

This article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as...

Classical wavelet systems over finite fields

This article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. It is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...