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1. Small generators of abelian number fields NSTL国家科技图书文献中心

Widmer, Martin -  《Forum mathematicum》 - 2025,37(2) - 629～636 - 共8页

摘要：We show that for each abelian number field K |  of sufficiently large degree d there exists an |  element alpha is an element of K with K = Q(alpha) and | Delta K|(1/2d | ), where Delta(K) denotes the discriminant of K. This
关键词： Weil height |  small generators |  Ruppert's conjecture |  abelian number fields |  Linnik's theorem
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2. Reduction map in the higher K-theory of the rings of integers in number fields NSTL国家科技图书文献中心

Sahu, Soumyadip -  《Journal of pure and applied algebra》 - 2025,229(1) - 共22页

摘要： higher K-theory of the ring of integers in a number | This article studies the reduction maps in the |  field arising from the canonical reduction maps at |  nonzero prime ideals. It proves an explicit density |  estimate for the subset of primes where the images of a
关键词： K-theory of number fields |  Stable cohomology
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3. Moments of non-normal number fields-II NSTL国家科技图书文献中心

Krishnamoorthy, Kris... -  《Monatshefte fur Mathematik》 - 2025,206(3) - 583～596 - 共14页

摘要：Suppose K is a number field and aK(m | )$$end{document} is the number of integral ideals of | )documentclass[12pt]{minimal} usepackage{amsmath} usepackage | {wasysym} usepackage{amsfonts} usepackage{amssymb | } usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek
关键词： Moments |  Dedekind zeta-function |  Artin L functions
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4. Linear recurrent sequences providing decomposition law in number fields NSTL国家科技图书文献中心

Hori, Haruto |  Kida, Masanari -  《The Ramanujan journal》 - 2025,66(3) - 共17页

摘要：In their recent paper, Rosen, Takeyama, Tasaka | , and Yamamoto constructed recurrent sequences that |  provide a decomposition law of primes in a Galois |  extension. In this paper, we reconstruct their sequences |  via the representation theory of finite groups and
关键词： Galois extension |  Prime decomposition law |  Recurrent sequence |  Group determinant
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5. Constructing infinite families of number fields with given indices from quintinomials NSTL国家科技图书文献中心

El Fadil, Lhoussain |  Kchit, Omar -  《Mathematica Slovaca》 - 2025,75(1) - 29～44 - 共16页

摘要： infinite families of number fields defined by | In this paper, for any rational prime p and |  for a fixed positive integer nu p, we provide |  quintinomials satisfying nu p(i(K)) = nu p. We illustrate our |  results by some computational examples.
关键词： Theorem of Dedekind |  Theorem of Ore |  prime ideal factorization |  Newton polygon |  index of a number field |  monogenic
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6. ON INDEX DIVISORS OF CERTAIN NUMBER FIELDS DEFINED BY x 11 + ax 2 + b NSTL国家科技图书文献中心

Kchit, Omar -  《Journal of the Korean Mathematical Society》 - 2025,62(1) - 197～216 - 共20页

摘要： Narkiewicz ([20]) for this family of number fields. As an | In this paper, for any number field K |  generated by a root alpha of a monic irreducible trinomial |  F(x) = x(11) + ax(2) + b is an element of Z [x | ] and for every rational prime p, we characterize when
关键词： Theorem of Dedekind |  theorem of Ore |  prime ideal factorization |  Newton polygon |  index of a number field |  power integral basis |  monogenic
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7. On extensions of number fields with given quadratic algebras and cohomology NSTL国家科技图书文献中心

Hamza, Oussama -  《Manuscripta mathematica》 - 2025,176(1) - 共21页

摘要： fields with prescribed ramification and splitting. | We introduce a criterion on the presentation |  of finitely presented pro-p groups which allows us |  to compute their cohomology groups and infer non | -analytic quotients, with cohomological dimension strictly
关键词： 12G10 |  20J05 |  20F05 |  20F40 |  17A45
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8. Explicit bounds for the solutions of superelliptic equations over number fields NSTL国家科技图书文献中心

Berczes, Attila |  Bugeaud, Yann... -  《Forum mathematicum》 - 2025,37(1) - 135～158 - 共24页

摘要： ring O-S of S-integers of a number field K, b a non | Let f be a polynomial with coefficients in the | -zero S-integer, and m an integer >= 2. We consider |  the following equation (*): f (x) = by(m) in x, y is |  an element of O-S. Under the well-known LeVeque
关键词： Superelliptic equation |  Thue equation |  Baker's method |  height function
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9. A new family of imaginary quadratic fields with class number divisible by 5 NSTL国家科技图书文献中心

Jin, Seokho |  Kim, Kwang-Seob -  《The Ramanujan journal》 - 2025,66(3) - 共10页

摘要： number in Fibonacci sequence. In this paper, we prove |  that the class number of Q(-Ds)documentclass[12pt |  Kishi's method in (J Number Theory 128, 2450-2458, 2008). | Let Dsdocumentclass[12pt]{minimal} usepackage | {amsmath} usepackage{wasysym} usepackage{amsfonts
关键词： Class number |  Quadratic fields
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10. On well-rounded lattices and lower bounds for the minimum norm of ideal lattices NSTL国家科技图书文献中心

Alves, Carina |  Strapasson, Joao E.... -  《Archiv der Mathematik》 - 2025,124(2) - 121～130 - 共10页

摘要： for mixed number fields through the canonical |  number field is cyclotomic. Additionally, we derive new | In this paper, we study properties of well | -rounded ideal lattices focusing on the lower bounds for |  their minimum norm. We present counterexamples showing
关键词： Ideal lattices |  Well-rounded lattices |  Minimum norm |  Number fields |  Cyclotomic fields
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