Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: For which p-adic integers x can Sum_k binomial(x,k)^(-1) be defined?   Let f(n)= Sum binomial(n,k)^(-1). First, we show that f:N to Q_p is nowhere
continuous in the p-adic topology. If x is a p-adic integer, we say that f(x)
is p-definable if lim f(x_j) exists in Q_p, where x_j denotes the jth partial
sum for x. We prove that f(-1) is p-definable for all primes p, and if p is
odd, then -1 is the only element of Z_p - N for which f(x) is p-definable. For
p=2, we show that if k is a positive integer, then f(-k-1) is not 2-definable,
but that if the 1's in the binary expansion of x are eventually very sparse,
then f(x) is 2-definable.
  Some of our proofs require that p satisfy one of two conditions. There are
three small primes that do not satisfy the relevant condition, but our theorems
can be proved directly for these primes. No other prime less than 100,000,000
fails to satisfy the conditions.

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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org