p-Fractals and Power Series - I Some 2 Variable Results
نویسندگان
چکیده
u1, . . . , ur are in kJx1, . . . , xsK with k and deg(u1, . . . , ur) finite. Intending applications to Hilbert-Kunz theory, we code the numbers deg(u1 1 , . . . , u ar r ) into a function φu, which empirically satisfies many functional equations related to “magnification by p”, where p = chark. p-fractals, introduced here, formalize these ideas. In the first interesting case (r = 3, s = 2), the φu are p-fractals. Our proof uses functions φI attached to ideals I and square-free elements h of A = kJx, yK. The finiteness of the set of ideal classes in A/(h) and the existence of “magnification maps” on this set show the φI to be p-fractals. We describe further functional equations coming from a theory of reflection maps on ideal classes, and the paper concludes with examples and open questions.
منابع مشابه
p-Fractals and power series–II. Some applications to Hilbert-Kunz theory
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