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Full-Text Articles in Number Theory
The Distribution Of Totally Positive Integers In Totally Real Number Fields, Tianyi Mao
The Distribution Of Totally Positive Integers In Totally Real Number Fields, Tianyi Mao
Dissertations, Theses, and Capstone Projects
Hecke studies the distribution of fractional parts of quadratic irrationals with Fourier expansion of Dirichlet series. This method is generalized by Behnke and Ash-Friedberg, to study the distribution of the number of totally positive integers of given trace in a general totally real number field of any degree. When the number field is quadratic, Beck also proved a mean value result using the continued fraction expansions of quadratic irrationals. We generalize Beck’s result to higher moments. When the field is cubic, we show that the asymptotic behavior of a weighted Diophantine sum is related to the structure of the unit …
Highly Degenerate Quadratic Forms Over Finite Fields Of Characteristic 2, Robert W. Fitzgerald
Highly Degenerate Quadratic Forms Over Finite Fields Of Characteristic 2, Robert W. Fitzgerald
Articles and Preprints
Let K/F be an extension of finite fields of characteristic two. We consider quadratic forms written as the trace of xR(x), where R(x) is a linearized polynomial. We show all quadratic forms can be so written, in an essentially unique way. We classify those R, with coefficients 0 or 1, where the form has a codimension 2 radical. This is applied to maximal Artin-Schreier curves and factorizations of linearized polynomials.