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We exhibit central simple algebras over the function field of a diagonal quartic surface over the complex numbers that represent the 2-torsion part of its Brauer group. We investigate whether the 2-primary part of the Brauer group of a diagonal quartic sur ...
Realistic models of particle physics include many scalar fields. These fields generically have nonminimal couplings to the Ricci curvature scalar, either as part of a generalized Einstein theory or as necessary counterterms for renormalization in curved ba ...
We explore the Mellin representation of conformal correlation functions recently proposed by Mack. Examples in the AdS/CFT context reinforce the analogy between Mellin amplitudes and scattering amplitudes. We conjecture a simple formula relating the bulk s ...
In this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields define ...
We show that the prime divisors of a random polynomial in F-q[t] are typically "Poisson distributed". This result is analogous to the result in Z of Granville [1]. Along the way, we use a sieve developed by Granville and Soundararajan [2] to give a simple ...
Based on truncated inverse filtering, a theory for deconvolution of complex fields is studied. The validity of the theory is verified by comparing with experimental data from digital holographic microscopy (DHM) using a high-NA system (NA=0.95). Comparison ...
We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common zero of the polynom ...
In this paper we investigate the efficiency of the function field sieve to compute discrete logarithms in the finite fields F3n. Motivated by attacks on identity based encryption systems using supersingular elliptic curves, we pay special at ...
We design algorithms for finding roots of polynomials over function fields of curves. Such algorithms are useful for list decoding of Reed-Solomon and algebraic-geometric codes. In the first half of the paper we will focus on bivariate polynomials, i.e., p ...
We generalize Sudan's (see J. Compl., vol.13, p.180-93, 1997) results for Reed- Solomon codes to the class of algebraic-geometric codes, designing algorithms for list decoding of algebraic geometric codes which can decode beyond the conventional error-corr ...
