Results 21 to 30 of about 387,449 (281)
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
core +1 more source
On the Units of Algebraic Number Fields
Journal of Number Theory, 1994 Let \(K\) be an algebraic number field of degree \(n\) over the rational number field and \(k\) be a proper subfield of \(K\) with \([K: k]=m\). Further, let \(R_ 1\), \(r_ 1\) denote the number of embeddings of \(K\), \(k\) into the real numbers and \(2R_ 2\), \(2r_ 2\) denote the numbers of embeddings of \(K\), \(k\) into the complex numbers.
Yamaguchi, I., Takeuchi, H.
openaire +2 more sources
Propulsion and Power Research, 2021 Time-dependent viscous fluid flow due to a stretchable rotating disk is investigated. Magnetic field is applied in vertical direction to the disk. Temperature equation is assisted with Joule heating effect.
Salman Ahmad +4 more
doaj +1 more source
Arithmetic of Calabi-Yau Varieties and Rational Conformal Field Theory [PDF]
, 2001 It is proposed that certain techniques from arithmetic algebraic geometry provide a framework which is useful to formulate a direct and intrinsic link between the geometry of Calabi-Yau manifolds and the underlying conformal field theory. Specifically it
Candelas +16 more
core +2 more sources
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
doaj +1 more source
On a theorem of Ax and Katz [PDF]
, 2015 The well-known theorem of Ax and Katz gives a p-divisibility bound for the number of rational points on an algebraic variety V over a finite field of characteristic p in terms of the degree and number of variables of defining polynomials of V.
Zhu, Hui June
core +4 more sources
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
doaj +1 more source
The Genus Field and Genus Number in Algebraic Number Fields [PDF]
Nagoya Mathematical Journal, 1967 Let k be an algebraic number field and K be its normal extension of finite degree. Then the genus field K* of K over k is defined as the maximal unramified extension of K which is obtained from K by composing an abelian extension over k2). We call the degree (K*: K) the genus number of K over k.
openaire +2 more sources
Nontrivial Galois module structure of cyclotomic fields [PDF]
, 2002 We say a tame Galois field extension $L/K$ with Galois group $G$ has trivial Galois module structure if the rings of integers have the property that $\Cal{O}_{L}$ is a free $\Cal{O}_{K}[G]$-module.
Conrad, Marc, Replogle, Daniel R.
core +5 more sources
Integral points of fixed degree and bounded height [PDF]
, 2015 By Northcott's Theorem there are only finitely many algebraic points in affine $n$-space of fixed degree over a given number field and of height at most $X$. For large $X$ the asymptotics of these cardinalities have been investigated by Schanuel, Schmidt,
Widmer, Martin
core +2 more sources