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136,685
Modular elliptic curves and Fermat’s Last Theorem
 ANNALS OF MATH
, 1995
"... When Andrew John Wiles was 10 years old, he read Eric Temple Bell’s The Last Problem and was so impressed by it that he decided that he would be the first person to prove Fermat’s Last Theorem. This theorem states that there are no nonzero integers a, b, c, n with n> 2 such that a n + b n = c n ..."
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Cited by 606 (1 self)
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When Andrew John Wiles was 10 years old, he read Eric Temple Bell’s The Last Problem and was so impressed by it that he decided that he would be the first person to prove Fermat’s Last Theorem. This theorem states that there are no nonzero integers a, b, c, n with n> 2 such that a n + b n = c
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 547 (59 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a
Common Risk Factors in the Returns On Stocks And Bonds
 Journal of Financial Economics
, 1993
"... This paper identities five common risk factors in the returns on stocks and bonds. There are three stockmarket factors: an overall market factor and factors related to firm size and booktomarket equity. There are two bondmarket factors. related to maturity and default risks. Stock returns have s ..."
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Cited by 1781 (29 self)
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This paper identities five common risk factors in the returns on stocks and bonds. There are three stockmarket factors: an overall market factor and factors related to firm size and booktomarket equity. There are two bondmarket factors. related to maturity and default risks. Stock returns have shared variation due to the stockmarket factors, and they are linked to bond returns through shared variation in the bondmarket factors. Except for lowgrade corporates. the bondmarket factors capture the common variation in bond returns. Most important. the five factors seem to explain average returns on stocks and bonds. 1.
Some optimal inapproximability results
, 2002
"... We prove optimal, up to an arbitrary ffl? 0, inapproximability results for MaxEkSat for k * 3, maximizing the number of satisfied linear equations in an overdetermined system of linear equations modulo a prime p and Set Splitting. As a consequence of these results we get improved lower bounds for ..."
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Cited by 779 (12 self)
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We prove optimal, up to an arbitrary ffl? 0, inapproximability results for MaxEkSat for k * 3, maximizing the number of satisfied linear equations in an overdetermined system of linear equations modulo a prime p and Set Splitting. As a consequence of these results we get improved lower bounds
Handbook of Applied Cryptography
, 1997
"... As we draw near to closing out the twentieth century, we see quite clearly that the informationprocessing and telecommunications revolutions now underway will continue vigorously into the twentyfirst. We interact and transact by directing flocks of digital packets towards each other through cybers ..."
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Cited by 3180 (33 self)
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As we draw near to closing out the twentieth century, we see quite clearly that the informationprocessing and telecommunications revolutions now underway will continue vigorously into the twentyfirst. We interact and transact by directing flocks of digital packets towards each other through cyberspace, carrying love notes, digital cash, and secret corporate documents. Our personal and economic lives rely more and more on our ability to let such ethereal carrier pigeons mediate at a distance what we used to do with facetoface meetings, paper documents, and a firm handshake. Unfortunately, the technical wizardry enabling remote collaborations is founded on broadcasting everything as sequences of zeros and ones that one's own dog wouldn't recognize. What is to distinguish a digital dollar when it is as easily reproducible as the spoken word? How do we converse privately when every syllable is bounced off a satellite and smeared over an entire continent? How should a bank know that it really is Bill Gates requesting from his laptop in Fiji a transfer of $10,000,000,000 to another bank? Fortunately, the magical mathematics of cryptography can help. Cryptography provides techniques for keeping information secret, for determining that information
BASIC CONCEPTS OF ENRICHED CATEGORY THEORY
 REPRINTS IN THEORY AND APPLICATIONS OF CATEGORIES
, 2005
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Efficient dispersal of information for security, load balancing, and fault tolerance
 Journal of the ACM
, 1989
"... Abstract. An Information Dispersal Algorithm (IDA) is developed that breaks a file F of length L = ( F ( into n pieces F,, 1 5 i 5 n, each of length ( F, 1 = L/m, so that every m pieces suffice for reconstructing F. Dispersal and reconstruction are computationally efficient. The sum of the lengths ..."
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Cited by 548 (1 self)
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Abstract. An Information Dispersal Algorithm (IDA) is developed that breaks a file F of length L = ( F ( into n pieces F,, 1 5 i 5 n, each of length ( F, 1 = L/m, so that every m pieces suffice for reconstructing F. Dispersal and reconstruction are computationally efficient. The sum of the lengths
Results 1  10
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136,685