Counting perfect polynomials
نویسندگان
چکیده
Let A ∈ F2[T ]. We say A is perfect if A coincides with the sum of all of its divisors in F2[T ]. We prove that the number of perfect polynomials A with |A| ≤ x is O (x1/12+ ) for all > 0, where |A| = 2degA. We also prove that every perfect polynomial A with 1 < |A| ≤ 1.6× 1060 is divisible by T or T + 1; that is, there are no small “odd” perfect polynomials.
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ورودعنوان ژورنال:
- Finite Fields and Their Applications
دوره 47 شماره
صفحات -
تاریخ انتشار 2017