# P-Adic L-Functions Pt I

## Introductory Workshop: Algebraic Cycles, L-Values, and Euler Systems January 23, 2023 - January 27, 2023

**Speaker(s):**Zheng Liu (University of California, Santa Barbara)

**Location:**SLMath: Eisenbud Auditorium, Online/Virtual

**Primary Mathematics Subject Classification**No Primary AMS MSC

**Secondary Mathematics Subject Classification**No Secondary AMS MSC

#### P-Adic L-Functions Pt I

I will give an introduction to p-adic L-functions. I will explain the conjecture by Coates and Perrin-Riou on the existence of p-adic L-functions and their definition of the modified Euler factors at p for p-adic interpolations. I will also talk about some approaches for constructing p-adic L-functions with some examples.

#### P-Adic L-Functions Pt I

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