Search

Summary

Ordinary probabilities are real numbers, and ordinary entropy is a real number too. Building on ideas of Kontsevich, we develop an analogue of entropy in which both the probabilities and entropy itself are integers modulo a prime number p. While the formula for entropy mod p is quite unlike the formula for real entropy, we prove characterization theorems for entropy mod p and information loss mod p that are very closely analogous to the theorems over the real numbers, thus justifying the definition. We also establish a sense in which entropy mod p is the residue mod p of real entropy.

The generalized Soulé character was introduced by H. Nakamura and Z. Wojtkowiak and is a generalization of Soulé’s cyclotomic character. In this paper, we prove that certain linear sums of generalized Soulé characters essentially coincide with the image of generalized Beilinson elements in K-groups under Soulé’s higher regulator maps. This result generalizes Huber–Wildeshaus’ theorem, which is a cyclotomic field case of our results, to an arbitrary number fields.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

11 - Entropy Modulo a Prime

Summary

Generalized Beilinson Elements and Generalized Soulé Characters

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

11 - Entropy Modulo a Prime

Summary

Generalized Beilinson Elements and Generalized Soulé Characters