On unit root formulas for toric exponential sums

Alan Adolphson, Steven Sperber

Research output: Contribution to journalArticlepeer-review

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Starting from a classical generating series for Bessel functions due to Schlömilch, we use Dwork's relative dual theory to broadly generalize unit-root results of Dwork on Kloosterman sums and Sperber on hyperkloosterman sums. In particular, we express the (unique) p-adic unit root of an arbitrary exponential sum on the torus T n in terms of special values of the p-adic analytic continuation of a ratio of A-hypergeometric functions. In contrast with the earlier works, we use noncohomological methods and obtain results that are valid for arbitrary exponential sums without any hypothesis of nondegeneracy.

Original languageEnglish (US)
Pages (from-to)573-585
Number of pages13
JournalAlgebra and Number Theory
Issue number3
StatePublished - 2012


  • A-hypergeometric functions
  • Exponential sums

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