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Singularities of bessel-zeta functions and Hawkins' polynomials

  • Kenneth B. Stolarsky (a1)

Abstract

The asymptotic behaviour of a sequence of polynomials cm = cm(v) satisfying

is established. These polynomials occur in Hawkins' formula for the residues of a Bessel-zeta function at its possible poles in the left half plane. The results imply that cm(v)/cm(0) converges uniformly to cos πV on compact sets. This in turn implies that, for v not a half odd integer, all but finitely many of the possible poles are actual poles.

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