Abstract
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 language | English (US) |
---|---|
Pages (from-to) | 129-156 |
Number of pages | 28 |
Journal | Pacific Journal of Mathematics |
Volume | 288 |
Issue number | 1 |
DOIs | |
State | Published - 2017 |
Bibliographical note
Publisher Copyright:© 2017 Mathematical Sciences Publishers.
Keywords
- Hypergeometric
- L-function
- Unit root