On testing the divisibility of lacunary polynomials by cyclotomic polynomials (2008)
Michael Filaseta, Andrzej Schinzel
Abstract. An algorithm is described that determines whether a given polynomial with integer coefficients has a cyclotomic factor. The algorithm is intended to be used for sparse polynomials given as...
Dedicated to the memory of Emil Grosswald (2008)
Michael Filaseta, Ognian Trifonov
In 1951, Emil Grosswald [7] began investigating the irreducibility of the Bessel Polynomials nX (n + j)! yn(x) = 2j (n, j)!j! xj:
On the factorization of polynomials with small Euclidean norm (2007)
this paper, we refer to the non-cyclotomic part of a polynomial
Short Interval Results For ...-Free Values Of Irreducible Polynomials (2007)
Michael Filaseta, David R. Richman
this paper is to show that one can in general
Squarefree Values Of Polynomials (2007)
this paper is to present some results related to squarefree values of polynomials. For f(x) 2 Z[x] with f(x) 6j 0; we define N f = gcd(f(m); m 2 Z): For computational reasons it is worth noting that...
On testing the divisibility of lacunary polynomials by cyclotomic polynomials (2007)
Michael Filaseta, Andrzej Schinzel
This note describes an algorithm for determining whether a given polynomial f(x) 2 Z[x] has a cyclotomic divisor. In particular, the algorithm works well
A Distribution Problem for Powerfree Values of Irreducible Polynomials (2007)
Brian Beasley, Michael Filaseta
: To better understand the distribution of gaps between k- free numbers, Erd}os posed the problem of establishing an asymptotic formula for the sum of the powers of the lengths of the gaps between...
Supercomputing Research Center Bowie, Maryland January 1992 (2007)
Ua Ry, Michael Filaseta, M. L. Robinson, Ferrell S. Wheeler
. For P 2 Z[x], let kPk denote the Euclidean norm of the coefficient vector of P . For an algebraic number ff, with minimal polynomial A, define the Euclidean norm of ff by kffk = kkAk ; where k is...
On A Limit Point Associated With The abc-Conjecture (2007)
Michael Filaseta, Sergei Konyagin, Theorem S
9.89> T 1; 3 2 ' 6= ;. In other words, we prove that there is a limit point of fL a;b g somewhere in the interval [1; 3=2). Before proving the theorem, it is of some value to discuss simpler...
Irreducibility Testing of Lacunary 0,1-Polynomials (2007)
Michael Filaseta, Douglas B. Meade
1 The first author was supported by grants from the National Security Agency.
Irreducibility Testing of Lacunary 0,1-Polynomials (2007)
Michael Filaseta, Douglas B. Meade
1 The rst author was supported by grants from the National Security Agency. 1
ON THE IRREDUCIBILITY OF A CERTAIN CLASS OF LAGUERRE POLYNOMIALS (2007)
Michael Filaseta, Richard L. Williams
The authors were supported by grants from the National Security Agency. Research by the second author associated with this paper was done in partial fulfillment of the requirement for a Ph.D. at the...
Irreducibility Testing of Lacunary 0,1-Polynomials (2007)
Michael Filaseta, Douglas B. Meade
1 The first author was supported by grants from the National Security Agency.
ON THE IRREDUCIBILITY OF A CERTAIN CLASS OF LAGUERRE POLYNOMIALS (2007)
Michael Filaseta, Richard L. Williams
this paper was done in partial fulfillment of the requirement for a Ph.D. at the University of South Carolina. 1
A generalization of a second irreducibility theorem of I. Schur (2007)
Martha Allen And, Martha Allen, Michael Filaseta
this paper is to establish a generalization of a second theorem of I. Schur. Namely, we prove Theorem 2. For n an integer 1, define + a 0 where the a j 's are arbitrary integers with = 1. Let k...
SIEVING BY LARGE INTEGERS AND COVERING SYSTEMS OF CONGRUENCES (2006)
Michael Filaseta, Sergei Konyagin, Gang Yu, Kevin Ford, Carl Pomerance
An old question of Erdős asks if there exists, for each number N, a finite set S of integers greater than N and residue classes r(n) (mod n) for n ∈ S whose union is Z. We prove that if � n∈S...
Sieving by large integers and covering systems of congruences (2005)
Filaseta, Michael, Ford, Kevin, Konyagin, Sergei, Pomerance, Carl, Yu, Gang
An old question of Erdos asks if there exists, for each number N, a finite set S of integers greater than N and residue classes r(n) mod n for n in S whose union is all the integers. We prove that if...
On the irreducibility of a truncated binomial expansion (2004)
Filaseta, Michael, Kumchev, Angel, Pasechnik, Dmitrii V.
Let P_nk(x) denote the sum of the lowest k+1 terms in the expansion of (1+x)^n. We investigate the irreducibility of P_nk(x) and more general univariate polynomials related to it. Polynomials P_nk(x)...
The purpose of this paper is to give a partially expository account of results related to coverings of the integers (defined below) while at the same time making some new observations concerning a...
The distribution of fractional parts with applications to gap results (1996)
Michael Filaseta, Ognian Trifonov
Let 5 and TV be positive real numbers, and let /: IR H- » R be any function. In this paper, we will obtain estimates for the size of the set {u E (TV, 2N]: ||/(w)ll < 8}, where u represents an...
Squarefree Values Of Polynomials All Of Whose Coefficients Are 0 And 1 (1996)
Michael Filaseta, Sergei Konyagin
this paper is to establish two results concerning the polynomials in S.
The irreducibility of all but finitely many Bessel polynomials (1995)
this paper, we prove that y n (x) is irreducible for all but finitely many (possibly 0) positive integers n. Although the current methods lead to an effective bound on the number of reducible y n...
The Distribution Of Fractional Parts With Applications To Gap Results In Number Theory (1994)
Michael Filaseta, Ognian Trifonov
this paper, we will obtain estimates for the size of the set fu 2 (N; 2N ] : jjf (u)jj ! ffi g, where u
Powerfree Values of Binary Forms (1994)
this paper, we will also consider f to be irreducible. We set n = deg f . For k = 2, this problem has recently become of interest partially because of its connection to the rank of elliptic curves as...
The Distribution of Squarefull Numbers in Short Intervals (1994)
Michael Filaseta, Ognian Trifonov
this paper so that, in particular, our results do not depend on the use of exponential sums. We shall refer to the result of Heath-Brown in [4] and to a result of Huxley in [5], and note here that...
On the Distribution of Gaps between Squarefree Numbers (1993)
this paper is to substantiate our new result. Professor Hooley has informed me that there are similarities between our methods as well as significant differences. To obtain our result, we will...
On Gaps Between Squarefree Numbers II (1992)
Michael Filaseta, Ognian Trifonov
this paper, the authors continue their work on the problem of finding an h = h(x)
A Generalization Of An Irreducibility Theorem Of I. Schur (1991)
Michael Filaseta, Heini Halberstam
this paper refers to irreducibility over the rationals. Some condition, such as ja 0 j = ja n j = 1, on the integers a j is necessary; otherwise, the irreducibility of all polynomials of the form...
An extension of a theorem of Ljunggren
Michael Filaseta, Junior Solan
this paper are essentially the same as those of Ljunggren. He presented some key ideas introducing reciprocal polynomials into the problem of determining how polynomials with small Euclidean norm...
The Irreducibility Of The Bessel Polynomials
Michael Filaseta, Ognian Trifonov
this paper, we resolve this conjecture and establish the following generalization.
The Irreducibility of the Bessel Polynomials
Michael Filaseta Mathematics, Michael Filaseta, Ognian Trifonov
In the early 1950's, Emil Grosswald began investigating the irreducibility of the Bessel polynomials y n (x) and conjectured the irreducibility of y n (x) over the rationals for all positive...