Luis A. Medina
Linear recurrences and asymptotic behavior of exponential sums of symmetric boolean functions.
Ср, 01/26/2011 - 16:01 — SomNambulAuthors: Luis A. Medina, Francis N. Castro
Subjects: Number Theory
AbstractIn this paper we give an improvement of the degree of the homogeneous linear
recurrence with integer coefficients that exponential sums of symmetric Boolean
functions satisfy. This improvement is tight. We also compute the asymptotic
behavior of symmetric Boolean functions and provide a formula that allows us to
determine if a symmetric boolean function is asymptotically not balanced. In
particular, when the degree of the symmetric function is a power of two, then
the exponential sum is much smaller than $2^n$.Iterated primitives of logarithmic powers.
Пнд, 11/09/2009 - 16:01 — SomNambulAuthors: Eric S. Rowland, Luis A. Medina, Victor H. Moll
Subjects: Number Theory
AbstractThe evaluation of iterated primitives of powers of logarithms is expressed in
closed form. The expressions contain polynomials with coefficients given in
terms of the harmonic numbers and their generalizations. The logconcavity of
these polynomials is established.p-regularity of the p-adic valuation of the Fibonacci sequence.
Пт, 10/16/2009 - 17:25 — SomNambulAuthors: Eric S. Rowland, Luis A. Medina
Subjects: Number Theory
AbstractThis paper studies the $p$-adic valuation of the sequence $\{F_n\}_{n \geq
1}$ of Fibonacci numbers from the perspective of regular sequences. We
establish that this sequence is $p$-regular for every prime $p$ and give an
upper bound on the rank for primes such that Wall's question has an affirmative
answer. We also point out that for primes $p \equiv 1,4 \mod 5$ the $p$-adic
valuation of $F_n$ depends only on the $p$-adic valuation of $n$ and on the sum
modulo $p-1$ of the base-$p$ digits of $n$ -- not the digits themselves or
their order.p-regularity of the p-adic valuation of the Fibonacci sequence.
Пт, 10/16/2009 - 17:25 — SomNambulAuthors: Eric S. Rowland, Luis A. Medina
Subjects: Number Theory
AbstractThis paper studies the $p$-adic valuation of the sequence $\{F_n\}_{n \geq
1}$ of Fibonacci numbers from the perspective of regular sequences. We
establish that this sequence is $p$-regular for every prime $p$ and give an
upper bound on the rank for primes such that Wall's question has an affirmative
answer. We also point out that for primes $p \equiv 1,4 \mod 5$ the $p$-adic
valuation of $F_n$ depends only on the $p$-adic valuation of $n$ and on the sum
modulo $p-1$ of the base-$p$ digits of $n$ -- not the digits themselves or
their order.
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