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Establish a corrected algebraic definition for the p-adic L-function associated with a motive over the rational field.

June 20, 2018Advanced studies in pure mathematics

On p-adic L-functions Attached to Motives over Q

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Establish a corrected algebraic definition for the p-adic L-function associated with a motive over the rational field.
Assumed the motive over the rational numbers admits at least one critical point.
Required that the selected prime number p is ordinary with respect to the motive.
Revised a previously established mathematical construction developed by Perrin-Riou and the author.
Formulated a rigorous definition for the p-adic L-function of ordinary motives.
Corrected the previous construction by introducing an explicit power factor of the imaginary unit i.

Implication

Mathematical analysis demonstrates an updated formulation for p-adic L-functions of motives over rational numbers, resolving a prior sign discrepancy.

Abstract

We propose a definition of thep-adic L-function of a motiveM over ℚ assumingM admits at least one critical point, andp is ordinary forM. This corrects by a power of\(i = √ - 1 \) an earlier definition of B. Perrin-Riou and the author.

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Cite This Study

Coates et al. (2018) studied this question.

synapsesocial.com/papers/6a04046d8235fcdee82b42d0 https://doi.org/10.2969/aspm/01710023

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Implication

Mathematical analysis demonstrates an updated formulation for p-adic L-functions of motives over rational numbers, resolving a prior sign discrepancy.

On p-adic L-functions Attached to Motives over Q

Key Points

Implication

Abstract

Discussion

Cite This Study

On p-adic L-functions Attached to Motives over Q

Key Points

Implication

Abstract

Discussion

Cite This Study

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