Corpus ID: 102352265

Note on Coleman's formula for the absolute Frobenius on Fermat curves

@article{Kashio2019NoteOC,
  title={Note on Coleman's formula for the absolute Frobenius on Fermat curves},
  author={Tomokazu Kashio},
  journal={arXiv: Number Theory},
  year={2019}
}
Coleman calculated the absolute Frobenius on Fermat curves explicitly. In this paper we show that a kind of $p$-adic continuity implies a large part of his formula. To do this, we study a relation between functional equations of the ($p$-adic) gamma function and monomial relations on ($p$-adic) CM-periods. 

References

SHOWING 1-10 OF 12 REFERENCES
On the regulator of Fermat motives and generalized hypergeometric functions
Abstract We calculate the Beilinson regulator of motives associated to Fermat curves and express them by special values of generalized hypergeometric functions. As a result, we obtain surjectivityExpand
Fermat curves and a refinement of the reciprocity law on cyclotomic units
  • Tomokazu Kashio
  • Mathematics
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
  • 2018
We define a “period-ring-valued beta function” and give a reciprocity law on its special values. The proof is based on some results of Rohrlich and Coleman concerning Fermat curves. We also haveExpand
On the periods of abelian integrals and a formula of Chowla and Selberg
Given an imaginary quadratic field k of discriminant d , let E be an elliptic curve defined over Q, the algebraic closure of Q in C, which admits complex multiplication by some order in k. Let ~ be aExpand
Absolute CM-periods
Introduction Multiple gamma function and its generalizations The Stark-Shintani conjecture Absolute CM-periods Explicit cone decompositions and applications Applications of a limit formula ofExpand
On p-adic absolute CM-periods I
The second author defined the absolute CM-period symbol using the multiple gamma function. This symbol is conjectured to give the same value as Shimura's period symbol up to multiplication byExpand
On a common refinement of Stark units and Gross-Stark units
The purpose of this paper is to formulate and study a common refinement of a version of Stark's conjecture and its $p$-adic analogue, in terms of Fontaine's $p$-adic period ring and $p$-adic HodgeExpand
On p-Adic Absolute CM-Periods II
In part I of this paper, we studied the p-adic absolute CM-period symbol in the completely split case. We presented a conjecture which predicts the exact value of this symbol with supportingExpand
Examples of CM curves of genus two defined over the reflex field
Van Wamelen [Math. Comp. 68 (1999) no. 225, 307–320] lists 19 curves of genus two over $\mathbf{Q}$ with complex multiplication (CM). However, for each curve, the CM-field turns out to be cyclicExpand
...
1
2
...