In [4], Ash and Sinnott conjecture that any Galois representation having niveau 1 which satisfies a certain parity condition is attached in a specific way to a Hecke eigenclass in cohomology, and they make a prediction about exactly where the relevant cohomology class should lie. They give examples of reducible three-dimensional representations which appear to be attached to cohomology eigencla...

In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions  for a weighted Lebesgue space  $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$.  Among the other things, we also show that if $K$ is a locally compact hyper...

let $r$ be an associative ring and let $m$ be a left $r$-module.let $spec_{r}(m)$ be the collection of all prime submodules of $m$ (equipped with classical zariski topology). there is a conjecture which says that every irreducible closed subset of $spec_{r}(m)$ has a generic point. in this article we give an affirmative answer to this conjecture and show that if $m$ has a noetherian spectrum, t...

Let λ denote the Liouville function. The Chowla conjecture, in the two-point correlation case, asserts that ∑ n6x λ(a1n + b1)λ(a2n + b2) = o(x) as x→∞, for any fixed natural numbers a1, a2 and nonnegative integer b1, b2 with a1b2−a2b1 6= 0. In this paper we establish the logarithmically averaged version ∑ x/ω(x)<n6x λ(a1n + b1)λ(a2n + b2) n = o(logω(x)) of the Chowla conjecture as x → ∞, where ...

amara in jurisprudential sources is said to any evidence which indicate the fact. indication is not definitively in the sight of foghaha and osooliyeen, but due to the prevailing conjecture which can be achieved from that evidence. witnesses’ testimony (bayyinah) as valid evidence in the jurisprudence and law is known as an “amara” in the sight of jurists witch its validity is from legislator. ...

A bstract We consider amplituhedron-like geometries which are defined in a similar way to the intrinsic definition of amplituhedron but with non-maximal winding number. propose that for cases minimal number points canonical form these corresponds product parity conjugate amplitudes at tree as well loop level. The superspace lifts star bosonised we give precise of. an alternative geometries, ana...

Consider an absolutely simple abelian variety X over a number field K. We show that if the absolute endomorphism ring of X is commutative and satisfies certain parity conditions, then Xp is absolutely simple for almost all primes p. Conversely, if the absolute endomorphism ring of X is noncommutative, then Xp is reducible for p in a set of positive density. An absolutely simple abelian variety ...

Quantum-dot Cellular Automata (QCA) is a prominent paradigm that is considered to continue its dominance in thecomputation at deep sub-micron regime in nanotechnology. The QCA realizations of five-input Majority Voter based multilevel parity generator circuits have been introduced in recent years. However, no attention has been paid towards the QCA instantiation of the generic (n-bit) even and ...

Quantum-dot Cellular Automata (QCA) is a prominent paradigm that is considered to continue its dominance in thecomputation at deep sub-micron regime in nanotechnology. The QCA realizations of five-input Majority Voter based multilevel parity generator circuits have been introduced in recent years. However, no attention has been paid towards the QCA instantiation of the generic (n-bit) even and ...