# New p-adic hypergeometric functions concerning with syntomic regulators

@article{Asakura2018NewPH, title={New p-adic hypergeometric functions concerning with syntomic regulators}, author={Masanori Asakura}, journal={arXiv: Algebraic Geometry}, year={2018} }

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.

## One Citation

Congruence relations for p-adic hypergeometric functions $$\widehat{{\mathscr {F}}}_{a,...,a}^{(\sigma )}(t)$$ and its transformation formula

- Mathematicsmanuscripta mathematica
- 2021

We introduce new kind of $p$-adic hypergeometric functions. We show these functions satisfy congruence relations, so they are convergent functions. And we show that there is a transformation formula…

## References

SHOWING 1-10 OF 22 REFERENCES

F-isocrystal and syntomic regulators via hypergeometric functions

- Mathematics
- 2017

We give an explicit description of a syntomic regulator of a certain class of fibrations which we call hypergeometric fibrations. The description involves hypergeometric functions.

Regulators of K_2 of Hypergeometric Fibrations

- Mathematics
- 2017

We discuss Beilinson's regulator on K_2 of certain fibrations of algebraic varieties which we call the hypergeomtric fibrations. The main result is to describe regulators via the hypergeometric…

Kato’s Euler system and rational points on elliptic curves I: A p-adic Beilinson formula

- Mathematics
- 2014

This article is the first in a series devoted to Kato’s Euler system arising from p-adic families of Beilinson elements in the K-theory of modular curves. It proves a p-adic Beilinson formula…

CM Periods, CM Regulators, and Hypergeometric Functions, I

- MathematicsCanadian Journal of Mathematics
- 2018

Abstract We prove the Gross–Deligne conjecture on CM periods for motives associated with ${{H}^{2}}$ of certain surfaces fibered over the projective line. Then we prove for the same motives a formula…

From L-series of elliptic curves to Mahler measures

- MathematicsCompositio Mathematica
- 2012

Abstract We prove the conjectural relations between Mahler measures and L-values of elliptic curves of conductors 20 and 24. We also present new hypergeometric expressions for L-values of elliptic…

On the periods of abelian integrals and a formula of Chowla and Selberg

- Mathematics
- 1978

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 a…

Integral Elements in K-Theory and Products of Modular Curves

- Mathematics
- 2000

In the first part of this paper we use de Jong’s method of alterations to contruct unconditionally ‘integral’ subspaces of motivic cohomology (with rational coefficients) for Chow motives over local…

p-adic Differential Equations

- Mathematics
- 2010

Preface Introductory remarks Part I. Tools of p-adic Analysis: 1. Norms on algebraic structures 2. Newton polygons 3. Ramification theory 4. Matrix analysis Part II. Differential Algebra: 5.…

RÉGULATEURS p-ADIQUES EXPLICITES POUR LE K2 DES COURBES ELLIPTIQUES par

- 2010

Résumé. — Dans cet article, nous utilisons le système d’Euler de Kato et la théorie de Perrin-Riou pour établir une formule reliant la valeur en 0 de la fonction L p-adique d’une courbe elliptique…

Arithmetic of Weil curves

- Mathematics
- 1974

w 2. Well Curves . . . . . . . . . . . . . . . . . . . . . . 4 (2.1) Deflmtions . . . . . . . . . . . . . . . . . . . . . 4 (2.2) The Winding Number . . . . . . . . . . . . . . . . 7 (2.3) The…