Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On sums of coefficients of polynomials related to the Borwein
  conjectures   Recently, Li obtained an asymptotic formula for a certain partial sum
involving coefficients for the polynomial in the First Borwein conjecture. As a
consequence, he showed the positivity of this sum. His result was based on a
sieving principle discovered by himself and Wan. In fact, Li points out in his
paper that his method can be generalized to prove an asymptotic formula for a
general partial sum involving coefficients for any prime $p>3$. In this work,
we extend Li's method to obtain asymptotic formula for several partial sums of
coefficients of a very general polynomial. We find that in the special cases
$p=3, 5$, the signs of these sums are consistent with the three famous Borwein
conjectures. Similar sums have been studied earlier by Zaharescu using a
completely different method. We also improve on the error terms in the
asymptotic formula for Li and Zaharescu. Using a recent result of Borwein, we
also obtain an asymptotic estimate for the maximum of the absolute value of
these coefficients for primes $p=2, 3, 5, 7, 11, 13$ and for $p>15$, we obtain
a lower bound on the maximum absolute value of these coefficients for
sufficiently large $n$.

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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin