Intersective $$S_n$$ S n polynomials with few irreducible factors
نویسندگان
چکیده
منابع مشابه
Finite p-groups with few non-linear irreducible character kernels
Abstract. In this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.
متن کاملIntersective polynomials and the polynomial Szemerédi theorem
Let P = {p1, . . . , pr} ⊂ Q[n1, . . . , nm] be a family of polynomials such that pi(Z) ⊆ Z, i = 1, . . . , r. We say that the family P has the PSZ property if for any set E ⊆ Z with d∗(E) = lim supN−M→∞ |E∩[M,N−1]| N−M > 0 there exist infinitely many n ∈ Zm such that E contains a polynomial progression of the form {a, a + p1(n), . . . , a + pr(n)}. We prove that a polynomial family P = {p1, . ...
متن کاملComputing Polynomials with Few Multiplications
It is a folklore result in arithmetic complexity that the number of multiplication gates required to compute a worst-case n-variate polynomial of degree d is at least
متن کاملParity of the number of irreducible factors for composite polynomials
Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role. In this paper we consider discriminants of the composition of some polynomials over finite fields. The ...
متن کاملT. N. Shorey’s Influence in the Theory of Irreducible Polynomials
The idea of looking at the prime factorization of the coefficients of a polynomial in Z[x] in order to establish its irreducibility (over Q) goes back to the classical Schönemann-Eisenstein criterion first derived in [29] and [6] in the middle of the 19th century. At the beginning of the 20th century, G. Dumas [5], again making use of primes that divide the coefficients of a polynomial, introdu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: manuscripta mathematica
سال: 2016
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-016-0848-9