# CM Periods, CM Regulators, and Hypergeometric Functions, I

@article{Asakura2018CMPC, title={CM Periods, CM Regulators, and Hypergeometric Functions, I}, author={Masanori Asakura and Noriyuki Otsubo}, journal={Canadian Journal of Mathematics}, year={2018}, volume={70}, pages={481 - 514} }

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 which expresses the ${{K}_{1}}$ -regulators in terms of hypergeometric functions $_{3}{{F}_{2}}$ , and obtain a new example of non-trivial regulators.

## 11 Citations

CM periods, CM regulators and hypergeometric functions, II

- Mathematics
- 2018

We study periods and regulators of a certain class of fibrations of varieties whose relative $$H^1$$H1 has multiplication by a number field. Both are written in terms of values of hypergeometric…

AN ALGEBRO-GEOMETRIC STUDY OF SPECIAL VALUES OF HYPERGEOMETRIC FUNCTIONS $_{3}F_{2}$

- MathematicsNagoya Mathematical Journal
- 2018

For a certain class of hypergeometric functions $_{3}F_{2}$ with rational parameters, we give a sufficient condition for the special value at $1$ to be expressed in terms of logarithms of algebraic…

Regulators of $$K_2$$K2 of hypergeometric fibrations

- Mathematics
- 2018

We describe Beilinson regulators of hypergeometric fibrations in terms of generalized hypergeometric functions. Employing a formula of Rogers and Zudilin, we obtain the comparison of the regulator…

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…

Explicit logarithmic formulas of special values of hypergeometric functions 3F2

- MathematicsCommunications in Contemporary Mathematics
- 2019

In [M. Asakura, N. Otsubo and T. Terasoma, An algebro-geometric study of special values of hypergeometric functions [Formula: see text], to appear in Nagoya Math. J.;…

A FUNCTIONAL LOGARITHMIC FORMULA FOR THE HYPERGEOMETRIC FUNCTION $_{3}F_{2}$

- MathematicsNagoya Mathematical Journal
- 2018

We give a sufficient condition for the hypergeometric function $_{3}F_{2}$ to be a linear combination of the logarithm of algebraic functions.

Regulators of K_1 of Hypergeometric Fibrations

- Mathematics
- 2017

We study a deformation of what we call hypergeometric fibrations. Its periods and K_1-regulators are described in terms of hypergeometric functions 3F2 in a variable given by the deformation…

New p-adic hypergeometric functions concerning with syntomic regulators

- Mathematics
- 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…

An algebro-geometric study of the unit arguments ${}_3F_2(1,1,q;a,b;1)$, I

- Mathematics
- 2016

Let $a$, $b$, $q$ be rational numbers such that none of $a$, $b$, $q$, $q-a$, $q-b$, $q-a-b$ is an integer. Then we prove, ${}_3F_2(1,1,q;a,b;1)$ is a $\overline{\mathbb{Q}}$-linear combination of…

A functional logarithmic formula for hypergeometric functions 3F2

- Mathematics
- 2018

We give a sufficient condition for that the hypergeometric function 3F2 is a linear combination of the logarithmic function. The proof is based on the regulator formula which we proved in another…

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