Results 71 to 80 of about 1,812,540 (189)

Class Numbers of Real Cyclotomic Fields of Conductor pq [PDF]

, 2009
The class numbers h+ of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows and that is why other methods have been developed, which approach the problem from ...
Agathocleous, Eleni
core   +1 more source

p$p$‐adic equidistribution and an application to S$S$‐units

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract We prove a Galois equidistribution result for torsion points in Gmn$\mathbb {G}_m^n$ in the p$p$‐adic setting for test functions of the form log|F|p$\log |F|_p$ where F$F$ is a nonzero polynomial with coefficients in the field of complex p$p$‐adic numbers.
Gerold Schefer
wiley   +1 more source

Hypergeometric motives from Euler integral representations

Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.
Abstract We revisit certain one‐parameter families of affine covers arising naturally from Euler's integral representation of hypergeometric functions. We introduce a partial compactification of this family. We show that the zeta function of the fibers in the family can be written as an explicit product of L$L$‐series attached to nondegenerate ...
Tyler L. Kelly, John Voight
wiley   +1 more source

Projective modules of group rings over quadratic number fields [PDF]

, 1994
Let K be a quadratic number field, Ok its ring of integers, and G a cyclic group of order prime p. In this thesis, we study the kernel group D(O(_K)G) and obtain a number of results concerning its order and structure. For K imaginary, we also investigate
Ahmed, Iftikhar
core  

Joint Blind Identification of Cyclic Codes and Synchronization Scramblers From Synchronous Scrambling Sequences of Cyclic Codes Based on Soft Decision Information

IET Communications, Volume 20, Issue 1, January/December 2026.
A communication model for collaborative and non‐collaborative scenarios is proposed, where the error correction code used by the transmitter is a cyclic code and the scrambler used is a synchronous scrambler. The contents of the dashed boxes are the tasks of the non‐collaborative receiver and our research targets the contents of the red boxes, that is,
Yong Ding, Lei Ye, Kun Han, Peng Wang, Li Yu, Jialong Zhan   +5 more
wiley   +1 more source

Good Integers: A Structural Review With Applications to Polynomial Factorization and Algebraic Coding Theory

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

On Cyclotomic Polynomial Coefficients

, 2020
For a positive integer n > 1 the n-th cyclotomic polynomial is defined by (Formula presented) where ς are the primitive n-th roots of unity. These polynomials are known to possess many interesting properties.
Andrica, D., Bagdasar, O.
core  

Feasibility of primality in bounded arithmetic

Forum of Mathematics, Sigma
We prove the correctness of the AKS algorithm [1] within the bounded arithmetic theory $T^{\text {count}}_2$ or, equivalently, the first-order consequences of the theory $\text {VTC}^0$ expanded by the smash function, which we denote by
Raheleh Jalali, Ondřej Ježil
doaj   +1 more source

Fast AVX-512 Implementation of the Optimal Ate Pairing on BLS12-381

Transactions on Cryptographic Hardware and Embedded Systems
Non-degenerate bilinear maps on elliptic curves, commonly referred to as pairings, have many applications including short signature schemes, zero-knowledge proofs and remote attestation protocols.
Hao Cheng, Georgios Fotiadis, Johann Großschädl, Daniel Page   +3 more
doaj   +1 more source

Sparse representation for cyclotomic fields

, 2008
. Currently, all major implementations of cyclotomic fields as well as number fields, are based on a dense model where elements are represented either as dense polynomials in the generator of the field or as coefficient vectors with respect to a fixed ...
Claus Fieker
core