Results 21 to 30 of about 4,688 (128)
A Study of Kummer's Proof of Fermat's Last Theorem for Regular Primes [PDF]
, 2013 We study Kummer's approach towards proving the Fermat's last Theorem for regular primes. Some basic algebraic prerequisites are also discussed in this report, and also a brief history of the problem is mentioned.
Saikia, Manjil P.
core
Arithmetic of characteristic p special L-values (with an appendix by V. Bosser)
, 2014 Recently the second author has associated a finite $\F_q[T]$-module $H$ to the Carlitz module over a finite extension of $\F_q(T)$. This module is an analogue of the ideal class group of a number field.
Anderson +27 more
core +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.For nonzero coprime integers a and b, a positive integer l is said to be good with respect to a and b if there exists a positive integer k such that l divides ak + bk. Since the early 1990s, the notion of good integers has attracted considerable attention from researchers. This continued interest stems from both their elegant number‐theoretic structure
Somphong Jitman, Anwar Saleh Alwardi
wiley +1 more source
Cyclotomic Classes in a Product of Finite Abelian Groups and Applications
Journal of Mathematics, Volume 2026, Issue 1, 2026.Cyclotomic classes of finite abelian groups have been extensively investigated for many decades, largely because of their nice algebraic structure and the breadth of their theoretical and practical applications. They naturally arise in diverse areas of mathematics, ranging from number theory and polynomial factorization to the decomposition of group ...
Somphong Jitman, Faranak Farshadifar
wiley +1 more source
Norm residue symbol and cyclotomic units [PDF]
Acta Arithmetica, 1995 Let \(\ell\geq 5\) be a prime, \(\zeta\) a primitive \(\ell\)th root of unity, \(\lambda=1-\zeta\) the prime dividing \(\ell\) in \(K=\mathbb{Q}(\zeta)\), \(C\) the group of cyclotomic units of \(K\), and \((\alpha,\beta)\) Hilbert's norm residue symbol in the completion of \(K\) at \((\lambda)\). \textit{G. Terjanian} [Acta Arith.
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Bases for cyclotomic units over function fields [PDF]
Journal of the Australian Mathematical Society, 2001 AbstractWe find a basis for the universal punctured even distribution and then a basis for the cyclotomic units over function fields.
Bae, S Bae, Sung-Han, Jung, H
openaire +2 more sources
The m$m$‐step solvable anabelian geometry of mixed‐characteristic local fields
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract Let K$K$ be a mixed‐characteristic local field. For an integer m⩾0$m \geqslant 0$, we denote by Km/K$K^m / K$ the maximal m$m$‐step solvable extension of K$K$, and by GKm$G_K^m$ the maximal m$m$‐step solvable quotient of the absolute Galois group GK$G_K$ of K$K$.
Seung‐Hyeon Hyeon
wiley +1 more source
A Cup Product in the Galois Cohomology of Number Fields
, 2002 Let K be a number field containing the group of n-th roots of unity and S a set of primes of K including all those dividing n and all real archimedean places.
McCallum, William G., Sharifi, Romyar T.
core +5 more sources
Note on Cyclotomic Units and Gauss Sums in Local Cyclotomic Fields
Journal of Number Theory, 2001 Let \(K\) be an imaginary abelian number field, let \(p\) be an odd prime, and let \(K_{\infty}=\cup K_n\) be the cyclotomic \(\mathbb Z_p\)-extension of \(K\). Assume that \(K\) contains a primitive \(p\)-th root of unity and that the exponent of Gal\((K/\mathbb Q)\) is \(p-1\). Let \(\mathcal U_n\) be the group of semi-local units of \(K_n\) at \(p\),
openaire +2 more sources
General Gate Teleportation and the Inner Structure of Its Clifford Hierarchies
Mathematical Methods in the Applied Sciences, Volume 48, Issue 17, Page 15985-15997, 30 November 2025.ABSTRACT The quantum gate teleportation mechanism allows for the fault‐tolerant implementation of “Clifford hierarchies” of gates assuming, among other things, a fault‐tolerant implementation of the Pauli gates. We discuss how this method can be extended to assume the fault‐tolerant implementation of any orthogonal unitary basis of operators, in such a
Samuel González‐Castillo +3 more
wiley +1 more source