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# ðŸ“™ The Development of the Number Field Sieve by Arjen K. Lenstra, Hendrik W.Jr. Lenstra â€” free epub

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The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature.

## About book:

## About file:

Security code:

- Author:
**Arjen K. Lenstra, Hendrik W.Jr. Lenstra** - Year:
**1993** - Publisher:
**Springer** - Language:
**English** - ISBN:
**3540570136**

- DPI:
**300** - File size:
**129 983** - Format:
**djvu**

Security code:

The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algori...

Number theory is one of the oldest and most appealing areas of mathematics. Computation has always played a role in number theory, a role which has increased dramatically in the last 20 or 30 years, both because of the advent of modern computers, and beca...

Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, "down-to-earth" manner. It thus avoids local methods, for example, and presents proofs in a way that highlights the imp...

Although a vast literature exists on the subject of RSA and public-key cryptography, until now there has been no single source that reveals recent developments in the area at an accessible level. Acclaimed author Richard A. Mollin brings together all of t...

The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic.Al...

This book is a translation into English of Hilbert's "Theorie der algebraischen Zahlkrper" best known as the "Zahlbericht", first published in 1897, in which he provided an elegantly integrated overview of the development of algebraic number theory up to ...

Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realization that the underlying princi...

This is the English translation of the original Japanese book. In this volume, "Fermat's Dream", core theories in modern number theory are introduced. Developments are given in elliptic curves, $p$-adic numbers, the $\zeta$-function, and the number fields...

Focuses on the construction of optimal investment strategies in a security market model where the prices follow diffusion processes. Beginning with presenting the complete Black-Scholes type model, the book moves on to incomplete models and models includi...

Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling, permit an understanding of the global behavior of economic systems without first having to work out a detailed microscopic descripti...

In the 2nd edition some sections of Part I are omitted for better readability, and a brand new chapter is devoted to volatility risk. As a consequence, hedging of plain-vanilla options and valuation of exotic options are no longer limited to the Black-Sch...

Efficient Methods for Valuing Interest Rate Derivatives provides an overview of the models that can be used for valuing and managing interest rate derivatives. Split into two parts, the first discusses and compares the traditional models, such as spot- an...

In Volatility and Correlation 2nd edition: The Perfect Hedger and the Fox , Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly succ...

The tasks of macroeconomics are to interpret observations on economic aggregates in terms of the motivations and constraints of economic agents and to predict the consequences of alternative hypothetical ways of administering government economic policy....

This book analyzes real options valuation for non-constant versus constant interest rates using simulation and historical backtesting. Several real options are investigated and combined with various pricing tools and stochastic term structure models. Inte...

Tremendous growth in the credit industry has spurred the need for Credit Scoring and Its Applications, the only book that details the mathematical models that help creditors make intelligent credit risk decisions. Creditors of all types make risk decis...