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The nilpotent structure of open-closed string field theory
Journal of High Energy Physics, 2023 In this note we revisit the homotopy-algebraic structure of oriented bosonic open-closed string field theory and we give a new compact formulation in terms of a single cyclic open-closed co-derivation which defines a single nilpotent structure describing
Carlo Maccaferri +2 more
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Bicyclic commutator quotients with one non-elementary component [PDF]
Mathematica Bohemica, 2023 For any number field $K$ with non-elementary $3$-class group ${\rm Cl}_3(K)\simeq C_{3^e}\times C_3$, $e\ge2$, the punctured capitulation type $\varkappa(K)$ of $K$ in its unramified cyclic cubic extensions $L_i$, $1\le i\le4$, is an orbit under the ...
Daniel C. Mayer
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Sums of units in function fields II - The extension problem [PDF]
, 2013 In 2007, Jarden and Narkiewicz raised the following question: Is it true that each algebraic number field has a finite extension L such that the ring of integers of L is generated by its units (as a ring)?
Frei, Christopher
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On the computation of the class number of an algebraic number field
, 1989 It is shown how the analytic class number formula can be used to produce an algorithm which efficiently computes the class number h of an algebraic number field F.
J. Buchmann, H. Williams
semanticscholar +1 more source
Tropical Effective Primary and Dual Nullstellens\"atze [PDF]
, 2015 Tropical algebra is an emerging field with a number of applications in various areas of mathematics. In many of these applications appeal to tropical polynomials allows to study properties of mathematical objects such as algebraic varieties and algebraic
Grigoriev, Dima, Podolskii, Vladimir V.
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The polylogarithm in algebraic number fields
Journal of Number Theory, 1985 AbstractBased on Kummer's 2-variable functional equations for the second through fifth orders of the polylogarithm function, certain linear combinations, with rational coefficients, of polylogarithms of powers of an algebraic base were discovered to possess significant mathematical properties. These combinations are designated “ladders,” and it is here
M.D. Abouzahra, L. Lewin
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Quantum spectral curve as a tool for a perturbative quantum field theory
Nuclear Physics B, 2015 An iterative procedure perturbatively solving the quantum spectral curve of planar N=4 SYM for any operator in the sl(2) sector is presented. A Mathematica notebook executing this procedure is enclosed.
Christian Marboe, Dmytro Volin
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Nonsplit conics in the reduction of an arithmetic curve
, 2021 For an algebraic function field $F/K$ and a discrete valuation $v$ of $K$ with perfect residue field $k$, we bound the number of discrete valuations on $F$ extending $v$ whose residue fields are algebraic function fields of genus zero over $k$ but not ...
Becher, Karim Johannes, Grimm, David
core
On the stufe of an algebraic number field
Journal of Number Theory, 1972 AbstractThe stufe, s = s(K), of a field K is the least number such that −1 is the sum of s squares of elements of K; then every element of K is the sum of s + 1 squares. Using the Hasse-Minkowski theorem on quadratic forms, and a simple algebraic identity, one can easily show that the stufe of an algebraic number field, if it exists, is 1, 2, or 4 ...
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Denominators of algebraic numbers in a number field
Journal of Number Theory, 2015 Abstract Text For any algebraic number γ, let g ( x ) be the unique irreducible polynomial with integral coefficients, whose leading coefficient c ( γ ) is positive, such that g ( γ ) = 0 . Let d ( γ ) be the denominator of γ. We fix a number field K, a prime p, a positive integer k and we study the set of values
Mohamed Ayad +2 more
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