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Probabilistic Number Theory by Elliott%2c Peter D

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1Probabilistic Number Theory

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  • Title: Probabilistic Number Theory
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 1053.49 Mbs, the file-s for this book were downloaded 104 times, the file-s went public at Thu Jul 18 2019.

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2A Structure Theorem In Probabilistic Number Theory

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We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the distribution of an additive function on the integers, and its distribution on the primes.

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  • Title: ➤  A Structure Theorem In Probabilistic Number Theory
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 5.41 Mbs, the file-s for this book were downloaded 104 times, the file-s went public at Mon Sep 23 2013.

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3Probabilistic Number Theory

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We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the distribution of an additive function on the integers, and its distribution on the primes.

“Probabilistic Number Theory” Metadata:

  • Title: Probabilistic Number Theory
  • Author:
  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 805.33 Mbs, the file-s for this book were downloaded 46 times, the file-s went public at Thu Jul 18 2019.

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4Number Theory Arising From Finite Fields : Analytic And Probabilistic Theory

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We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the distribution of an additive function on the integers, and its distribution on the primes.

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  • Title: ➤  Number Theory Arising From Finite Fields : Analytic And Probabilistic Theory
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 824.03 Mbs, the file-s for this book were downloaded 43 times, the file-s went public at Tue Jun 13 2023.

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5Quantum Probabilistic Subroutines And Problems In Number Theory

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We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for extracting the periodicity of a function, and their combined use in the counting algorithm originally introduced by Brassard et al. One of the main features of our quantum probabilistic algorithm is its full unitarity and reversibility, which would make its use possible as part of larger and more complicated networks in quantum computers. As an example of this we describe polynomial time algorithms for studying some important problems in number theory, such as the test of the primality of an integer, the so called 'prime number theorem' and Hardy and Littlewood's conjecture about the asymptotic number of representations of an even integer as a sum of two primes.

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  • Title: ➤  Quantum Probabilistic Subroutines And Problems In Number Theory
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 6.85 Mbs, the file-s for this book were downloaded 79 times, the file-s went public at Sat Sep 21 2013.

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