P-adic variation of unit root L-functions

C. Douglas Haessig, Steven Sperber

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Dwork's conjecture, now proven by Wan, states that unit root L-functions "coming from geometry" are p-adic meromorphic. In this paper we study the p-adic variation of a family of unit root L-functions coming from a suitable family of toric exponential sums. In this setting, we find that the unit root L-functions each have a unique p-adic unit root. We then study the variation of this unit root over the family of unit root L-functions. Surprisingly, we find that this unit root behaves similarly to the classical case of families of exponential sums, as studied by Adolphson and Sperber (2012). That is, the unit root is essentially a ratio of A-hypergeometric functions.

Original languageEnglish (US)
Pages (from-to)129-156
Number of pages28
JournalPacific Journal of Mathematics
Issue number1
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2017 Mathematical Sciences Publishers.


  • Hypergeometric
  • L-function
  • Unit root


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