• Corpus ID: 119609827

New p-adic hypergeometric functions concerning with syntomic regulators

  title={New p-adic hypergeometric functions concerning with syntomic regulators},
  author={Masanori Asakura},
  journal={arXiv: Algebraic Geometry},
  • M. Asakura
  • Published 9 November 2018
  • Mathematics
  • arXiv: Algebraic Geometry
We introduce new functions, which we call the p-adic hypergeometric functions of logarithmic type. We show the congruence relations that are similar to Dwork's. This implies that they are convergent functions, so that the special values at t=a with |a|=1 are defined under a mild condition. We then show that the special values appear in the syntomic regulators for hypergeometric curves. We expect that they agree with the special values of p-adic L-functions of elliptic curves in some cases. 
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