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ON THE ORDER OF UNIMODULAR MATRICES MODULO INTEGERS

Pär Kurlberg

Open publisher page 19 citations

Abstract

Assuming the Generalized Riemann Hypothesis, we prove the following: If b is an integer greater than one, then the multiplicative order of b modulo N is larger than N for all N in a density one subset of the integers. If A is a hyperbolic unimodular matrix with integer coecients, then the order of A modulo p is greater than p for all p in a density one subset of the primes. Moreover

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What this paper is about

Assuming the Generalized Riemann Hypothesis, we prove the following: If b is an integer greater than one, then the multiplicative order of b modulo N is larger than N for all N in a density one subset of the integers. If A is a hyperbolic unimodular matrix with integer coecients, then the order of A modulo p is greater than p for all p in a density one subset of the primes. Moreover

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OpenAlex reports 19 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Assuming the Generalized Riemann Hypothesis, we prove the following: If b is an integer greater than one, then the multiplicative order of b modulo N is larger than N for all N in a density one subset of the integers. If A is a hyperbolic unimodular matrix with integer coecients, then the order of A modulo p is greater than p for all p in a density one subset of the primes. Moreover

Key concepts: Mathematics, Unimodular matrix, Modulo, Order (exchange), Combinatorics, Pure mathematics, Economics, Finance

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