Results 1 - 10
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16,755
SPECIAL VALUES OF MULTIPLE POLYLOGARITHMS
, 1999
"... Historically, the polylogarithm has attracted specialists and nonspecialists alike withitslovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and high-energy physics. More recently, we ha ..."
Abstract
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Cited by 88 (23 self)
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Historically, the polylogarithm has attracted specialists and nonspecialists alike withitslovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and high-energy physics. More recently, we have been forced to consider multidimensional extensions encompassing the classical polylogarithm, Euler sums, and the Riemann zeta function. Here, we provide a general framework within which previously isolated results can now be properly understood. Applying the theory developed herein, we prove several previously conjectured evaluations, including an intriguing conjecture of Don Zagier.
Special Values of Multidimensional Polylogarithms
- TRANS. AMER. MATH. SOC
, 1998
"... Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and high-energy physics. More recently, w ..."
Abstract
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Cited by 20 (12 self)
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Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and high-energy physics. More recently, we have been forced to consider multidimensional extensions encompassing the classical polylogarithm, Euler sums, and the Riemann zeta function. Here, we provide a general framework within which previously isolated results can now be properly understood. Applying the theory developed herein, we prove several previously conjectured evaluations, including a longstanding conjec...
FUNCTORIALITY AND SPECIAL VALUES OF L-FUNCTIONS
"... Abstract. This is a semi-expository article concerning Langlands functoriality and Deligne’s conjecture on the special values of L-functions. The emphasis is on symmetric power L-functions associated to a holomorphic cusp form. Contents ..."
Abstract
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Cited by 5 (2 self)
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Abstract. This is a semi-expository article concerning Langlands functoriality and Deligne’s conjecture on the special values of L-functions. The emphasis is on symmetric power L-functions associated to a holomorphic cusp form. Contents
The Byzantine Generals Problem,"
- ACM Transactions on Programming Languages and Systems,
, 1982
"... Abstract The Byzantine Generals Problem requires processes to reach agreement upon a value even though some of them may fad. It is weakened by allowing them to agree upon an "incorrect" value if a failure occurs. The transaction eormmt problem for a distributed database Js a special case ..."
Abstract
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Cited by 1561 (6 self)
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Abstract The Byzantine Generals Problem requires processes to reach agreement upon a value even though some of them may fad. It is weakened by allowing them to agree upon an "incorrect" value if a failure occurs. The transaction eormmt problem for a distributed database Js a special case
Integral Motives and Special Values of . . .
, 2002
"... For each field k, we define a category of rationally decomposed mixed motives with Z-coefficients. When k is finite, we show that the category is Tannakian, and we prove formulas relating the behaviour of zeta functions near integers ..."
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For each field k, we define a category of rationally decomposed mixed motives with Z-coefficients. When k is finite, we show that the category is Tannakian, and we prove formulas relating the behaviour of zeta functions near integers
Special Values of Zeta:
"... s−1 1 1 ∞ x ζ () s = ∑ = dx (Re() s> 1) s 0 x n Γ s e −1 n= 1 s = σ + it (Complex variable) ..."
Abstract
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s−1 1 1 ∞ x ζ () s = ∑ = dx (Re() s> 1) s 0 x n Γ s e −1 n= 1 s = σ + it (Complex variable)
Results 1 - 10
of
16,755