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An ordinary cyclotomic function field
ordinary cyclotomic function field investigate $p$-rank
2012/3/1
In this paper, we investigate the $p$-rank of Jacobian of cyclotomic function field $K_m$. Our goal in this paper is to give the necessary and sufficient condition $m$ such that $K_m$ is ordinary.
A universal first order formula defining the ring of integers in a number field
universal first order formula defining ring integers number field
2012/3/1
We show that the complement of the ring of integers in a number field K is Diophantine. This means the set of ring of integers in K can be written as {t in K | for all x_1, ..., x_N in K, f(t,x_1, ......
Average estimate for additive energy in prime field
Average estimate additive energy prime field Number Theory
2011/9/19
Abstract: Assume that $A\subseteq \Fp, B\subseteq \Fp^{*}$, $\1/4\leqslant\frac{|B|}{|A|},$ $|A|=p^{\alpha}, |B|=p^{\beta}$. We will prove that for $p\geqslant p_0(\beta)$ one has $$\sum_{b\in B}E_{+}...
An algorithm for list decoding number field codes
algorithm number field codes Number Theory
2011/9/5
Abstract: We present an algorithm for list decoding codewords of algebraic number field codes in polynomial time. This is the first explicit procedure for decoding number field codes whose constructio...
Abstract: This is the text from a talk at the Arbeitstagung 2011, which can serve as an introduction to arxiv:1009.0736 and arXiv:1007.0907. I first discuss how a global field is determined by a certa...
Expansions of subfields of the real field by a discrete set
Expansions of subfields real field discrete set
2011/2/21
Let K be a subfield of the real field, D K be a closed and discrete set and f : Dn ! K be such that f(Dn) is somewhere dense. Then (K, f) defines Z. We present several applications of this result. W...
Field Extensions Having the Unique Subfield Property, and G-Cogalois Extensions
Field extension separable extension simple extension radical extension G--Cogalois extension unique subfield property classical Kummer extension
2010/3/1
We present a short proof, based on Cogalois Theory, of a result due to Acosta de Orozco and Vélez (1982, J. Number Theory 15, 388-405) characterizing separable simple radical field extensions with the...