Results 1 to 10 of about 1,187,567 (336)
Relative integral basis for algebraic number fields [PDF]
International Journal of Mathematics and Mathematical Sciences, 1986 At first conditions are given for existence of a relative integral basis for OK≅Okn−1⊕I with [K;k]=n. Then the constrtiction of the ideal I in OK≅Okn−1⊕I is given for proof of existence of a relative integral basis for OK4(m1,m2)/Ok(m3).
Mohmood Haghighi
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Improving the efficiency of using multivalued logic tools: application of algebraic rings [PDF]
Scientific Reports, 2023 It is shown that in order to increase the efficiency of using methods of abstract algebra in modern information technologies, it is important to establish an explicit connection between operations corresponding to various varieties of multivalued logics ...
Ibragim E. Suleimenov +3 more
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Computation of relative integral bases for algebraic number fields [PDF]
International Journal of Mathematics and Mathematical Sciences, 1988 At first we are given conditions for existence of relative integral bases for extension (K;k)=n. Then we will construct relative integral bases for extensions OK6(−36)/Ok2(−3), OK6(−36)/Ok3(−33), OK6(−36)/Z.
Mahmood Haghighi
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Lower bounds on the class number of algebraic function fields defined over any finite field [PDF]
arXiv, 2011 We give lower bounds on the number of effective divisors of degree $\leq g-1$ with respect to the number of places of certain degrees of an algebraic function field of genus $g$ defined over a finite field. We deduce lower bounds and asymptotics for the class number, depending mainly on the number of places of a certain degree.
Ballet, Stéphane, Rolland, Robert
arxiv +5 more sources
Character sums in algebraic number fields [PDF]
Journal of Number Theory, 1983 The Pólya-Vinogradov inequality is generalized to arbitrary algebraic number fields K of finite degree over the rationals. The proof makes use of Siegel's summation formula and requires results about Hecke's zeta-functions with Grössencharacters.
Hinz, Jürgen G
core +3 more sources
On the Units of Algebraic Number Fields
Journal of Number Theory, 1994 AbstractLet K be an algebraic number field and k be a proper subfield of K. Then we have the relations between the relative degree [K : k] and the increase of the rank of the unit groups. Especially, in the case of mth cyclotomic field Q(ζm), we determine the number m such that the increase of the rank of the unit groups is equal to the number of the ...
Itaru Yamaguchi, H. Takeuchi
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On computing the discriminant of an algebraic number field [PDF]
Mathematics of Computation, 1985 Let f ( x ) f(x) be a monic irreducible polynomial in Z [ x ] {\mathbf {Z}}[x] , and r a root of f ( x ) f(x) in C. Let K be the field Q (
Theresa P. Vaughan
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Fuchsian Groups and Algebraic Number Fields [PDF]
Transactions of the American Mathematical Society, 1985 Given the signature of a finitely-generated Fuchsian group, we find the minimal extension of the rationals for which there is a Fuchsian group having the required signature, whose matrix entries lie in this field.
P. L. Waterman, C. Maclachlan
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On the units of an algebraic number field [PDF]
Illinois Journal of Mathematics, 1965 James Ax
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Sequences of Residues in Algebraic Number Fields
Journal of Number Theory, 1995 AbstractWe define ΛF(n, m) for all integers n, m and an algebraic number field F to be the least positive number such that for almost all prime ideals p there are m consecutive nth power residues in the algebraic number field F with norm less than ΛF(n, m)[F : Q]. We prove several theorems based on these definitions.
A.M. Naranjani
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