7,820 research outputs found
Artin's primitive root conjecture -a survey -
This is an expanded version of a write-up of a talk given in the fall of 2000
in Oberwolfach. A large part of it is intended to be understandable by
non-number theorists with a mathematical background. The talk covered some of
the history, results and ideas connected with Artin's celebrated primitive root
conjecture dating from 1927. In the update several new results established
after 2000 are also discussed.Comment: 87 pages, 512 references, to appear in Integer
On quadratic progression sequences on smooth plane curves
We study the arithmetic (geometric) progressions in the -coordinates of
quadratic points on smooth projective planar curves defined over a number field
. Unless the curve is hyperelliptic, we prove that these progressions must
be finite. We, moreover, show that the arithmetic gonality of the curve
determines the infinitude of these progressions in the set of
-points with field of definition of degree at most ,
On the Divisibility of Trinomials by Maximum Weight Polynomials over F2
Divisibility of trinomials by given polynomials over finite fields has been
studied and used to construct orthogonal arrays in recent literature. Dewar et
al.\ (Des.\ Codes Cryptogr.\ 45:1-17, 2007) studied the division of trinomials
by a given pentanomial over \F_2 to obtain the orthogonal arrays of strength
at least 3, and finalized their paper with some open questions. One of these
questions is concerned with generalizations to the polynomials with more than
five terms. In this paper, we consider the divisibility of trinomials by a
given maximum weight polynomial over \F_2 and apply the result to the
construction of the orthogonal arrays of strength at least 3.Comment: 10 pages, 1 figur
Note on the Theory of Correlation Functions
The purpose of this note is to improve the current theoretical results for
the correlation functions of the Mobius sequence and the
Liouville sequence .Comment: Sixty Six Pages. Keywords: Autocorrelation function, Correlation
function, Multiplicative function, Liouville function, Mobius function, von
Mangoldt function, Exponential Su
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