Irreducibility criterion for certain trinomials

Abstract

In this article we study the irreducibility of polynomials of the form x n + ǫ 1 x m + p k ǫ 2 , p being a prime number. We will show that they are irreducible for m = 1. We have also provided the cyclotomic factors and reducibility criterion for trinomials of the formThis corrects few of the existing results of W. Ljuggren's on x n + ǫ 1 x m + ǫ 2 .

Fermion localization in a backreacted warped spacetime

“…where n = 1, 2, 3..... Now from the requirement of solving the gauge hierarchy problem, the warp factor at TeV brane acquires the value as A(π) = 36 which produces a large suppression in the right hand side of eqn. (22) through the exponential factor. Since k, m 5 ∼ M , the mass of KK modes (n = 1, 2, 3..) comes at TeV scale.…”

“…Moreover the mass squared gap (∆m 2 n = m 2 n+1 − m 2 n ) depends linearly on n which is also evident from the mass spectrum in eqn. (22).…”

“…In such a braneworld scenario, several models were proposed by placing the standard model fields inside the bulk . Specially the localization property of a bulk fermion field [18][19][20][21][22][23][24][25] has been a subject of great interest where explanations for observed chiral nature of massless fermion and the hierarchial masses of fermions among different generations have been explored. In this context, it is observed that the overlap of the bulk fermion wave function on our visible brane plays crucial role in determining the effective radion-fermion coupling which in turn determines phenomenology of the radion with brane matter fields.…”

Survey on irreducibility of trinomials

“…If k ≥ 2 and r = 0, then it is irreducible by Theorem 20. An alternate proof of this particular case can also be found in [65]. For k ≥ 2, r = 1, we will show that Theorem 21.…”

“…One can check that Ljunggren's result is true only when ǫ 1 = ǫ 2 = 1. We corrected these errors in [65] and proved that…”