Abstract
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) -adic unit root of an arbitrary exponential sum on the torus in terms of special values of the -adic analytic continuation of a ratio of -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.
Citation
Alan Adolphson. Steven Sperber. "On unit root formulas for toric exponential sums." Algebra Number Theory 6 (3) 573 - 585, 2012. https://doi.org/10.2140/ant.2012.6.573
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