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Arvind Kumar

Publications and source records attributed to Arvind Kumar.

At least 91 records · Page 5Linked to original sources
arXiv2022

$η$ meson in strange magnetized matter

The in-medium properties of $η$ mesons are studied in hot and dense isospin asymmetric strange magnetized matter using the chiral SU(3) hadronic mean-field model. The scalar and vector density of baryons are expressed in terms of thermal distribution functions at finite temperature and magnetic field and have dependence on the scalar fields $σ$, $ζ$, and $δ$ through the effective mass of baryons and the dependence on the vector fields $ω, ρ$, and $ϕ$ through the effective chemical potential. The properties of $η$ mesons get modified in a hot and dense magnetized environment through the medium-modified nucleons and hyperons. The negative mass shift obtained gives rise to optical potential, which is attractive in the medium and suggests a possibility of $η$-mesic bound states formation. The addition of hyperons in the medium enhances the attractive interactions and causes an increased negative mass shift for $η$ mesons.

hep-ph↗
arXiv2022

Ramanujan-style congruences for prime level

We establish Ramanujan-style congruences modulo certain primes $\ell$ between an Eisenstein series of weight $k$, prime level $p$ and a cuspidal newform in the $\varepsilon$-eigenspace of the Atkin-Lehner operator inside the space of cusp forms of weight $k$ for $Γ_0(p)$. Under a mild assumption, this refines a result of Gaba-Popa. We use these congruences and recent work of Ciolan, Languasco and the third author on Euler-Kronecker constants, to quantify the non-divisibility of the Fourier coefficients involved by $\ell.$ The degree of the number field generated by these coefficients we investigate using recent results on prime factors of shifted prime numbers.

math.NT↗
arXiv2022

On the resurgence and asymptotic resurgence of homogeneous ideals

Let $\mathbb{K}$ be a field and $R = \mathbb{K}[x_1, \ldots, x_n]$. We obtain an improved upper bound for asymptotic resurgence of squarefree monomial ideals in $R$. We study the effect on the resurgence when sum, product and intersection of ideals are taken. We obtain sharp upper and lower bounds for the resurgence and asymptotic resurgence of cover ideals of finite simple graphs in terms of associated combinatorial invariants. We also explicitly compute the resurgence and asymptotic resurgence of cover ideals of several classes of graphs. We characterize a graph being bipartite in terms of the resurgence and asymptotic resurgence of edge and cover ideals. We also compute explicitly the resurgence and asymptotic resurgence of edge ideals of some classes of graphs.

math.AC↗
arXiv2022

Reductions of Galois representations and the theta operator

Let $p\ge 5$ be a prime, and let $f$ be a cuspidal eigenform of weight at least $2$ and level coprime to $p$ of finite slope $α$. Let $\barρ_f$ denote the mod $p$ Galois representation associated with $f$ and $ω$ the mod $p$ cyclotomic character. Under an assumption on the weight of $f$, we prove that there exists a cuspidal eigenform $g$ of weight at least $2$ and level coprime to $p$ of slope $α+1$ such that $$\barρ_f \otimes ω\simeq \barρ_g,$$ up to semisimplification. The proof uses Hida-Coleman families and the theta operator acting on overconvergent forms. The structure of the reductions of the local Galois representations associated to cusp forms with slopes in the interval $[0,1)$ were determined by Deligne, Buzzard and Gee and for slopes in $[1,2)$ by Bhattacharya, Ganguli, Ghate, Rai and Rozensztajn. We show that these reductions, in spite of their somewhat complicated behavior, are compatible with the displayed equation above. Moreover, the displayed equation above allows us to predict the shape of the reductions of a class of Galois representations attached to eigenforms of slope larger than $2$. Finally, the methods of this paper allow us to obtain upper bounds on the radii of certain Coleman families.

math.NT↗
arXiv2022

On signs of Hecke eigenvalues of Siegel eigenforms

In this article, we distinguish Siegel cuspidal eigenforms of degree two on the full symplectic group from the signs of their Hecke eigenvalues. To establish our theorem, we obtain a result towards simultaneous sign changes of eigenvalues of two Siegel eigenforms. In the course of the proof, we also prove that the Satake $p$-parameters of two different Siegel eigenforms are distinct for a set of primes $p$ of density 1. The main ingredient to prove the latter result is the theory of Galois representations attached to Siegel eigenforms.

math.NT↗
arXiv2022

Coprimality of Fourier coefficients of eigenforms

Given a pair of distinct non-CM normalized eigenforms having integer Fourier coefficients $a_1 (n)$ and $a_2(n)$, we count positive integers $n$ with $(a_1(n), a_2(n))=1$ and make a conjecture about the density of the set of primes $p$ for which $(a_1(p), a_2(p))=1$. We also study the average order of the number of prime divisors of $(a_1(p), a_2(p))$.

math.NT↗
arXiv2022

A Search for Alternative Solid Rocket Propellant Oxidizers

Carbon-based caged and heterocyclic compounds tend to have strained molecular structures leading to high heats of formation and energetic behavior. In the current paper, molecular modelling calculations for 10 caged compounds of this type along with 2 strained aliphatic compounds and 4 simple cyclic chains are presented in view of their possible use as oxidizers in propulsion applications. Density functional theory (B3LYP) was employed for the geometry optimization of the proposed molecular structure using the 6-311++G(d,p) basis set. Heats of formation of the compounds were calculated using the molecular modeling results and their specific impulses were computed using the NASA CEA [1] software package to evaluate their potentials as propellant oxidizers.

cond-mat.mtrl-sci↗
arXiv2022

Recommendations for repositories and scientific gateways from a neuroscience perspective

Digital services such as repositories and science gateways have become key resources for the neuroscience community, but users often have a hard time orienting themselves in the service landscape to find the best fit for their particular needs. INCF (International Neuroinformatics Coordinating Facility) has developed a set of recommendations and associated criteria for choosing or setting up and running a repository or scientific gateway, intended for the neuroscience community, with a FAIR neuroscience perspective. These recommendations have neurosciences as their primary use case but are often general. Considering the perspectives of researchers and providers of repositories as well as scientific gateways, the recommendations harmonize and complement existing work on criteria for repositories and best practices. The recommendations cover a range of important areas including accessibility, licensing, community responsibility and technical and financial sustainability of a service.

cs.CY↗
arXiv2021

Binomial expansion for saturated and symbolic powers of sums of ideals

There are two different notions for symbolic powers of ideals existing in the literature, one defined in terms of associated primes, the other in terms of minimal primes. Elaborating on an idea known to Eisenbud, Herzog, Hibi, and Trung, we interpret both notions of symbolic powers as suitable saturations of the ordinary powers. We prove a binomial expansion formula for saturated powers of sums of ideals. This gives a uniform treatment to an array of existing and new results on both notions of symbolic powers of such sums: binomial expansion formulas, computations of depth and regularity, and criteria for the equality of ordinary and symbolic powers.

math.AC↗
arXiv2021

Rees algebra and special fiber ring of binomial edge ideals of closed graphs

In this article, we compute the regularity of Rees algebra of binomial edge ideals of closed graphs. We obtain a lower bound for the regularity of Rees algebra of binomial edge ideals. We also study some algebraic properties of the Rees algebra and special fiber ring of binomial edge ideals of closed graphs via algebraic properties of their initial algebra and Sagbi basis theory. We obtain an upper bound for the regularity of the special fiber ring of binomial edge ideals of closed graphs.

math.AC↗
arXiv2021

Upper bounds for the regularity of symbolic powers of certain classes of edge ideals

Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal in a polynomial ring over a field $\mathbb{K}$. In this paper, we obtain upper bounds for the Castelnuovo-Mumford regularity of symbolic powers of certain classes of edge ideals. We also prove that for several classes of graphs, the regularity of symbolic powers of their edge ideals coincides with that of their ordinary powers.

math.AC↗
arXiv2021

Binomial edge ideals and bounds for their regularity

Let $G$ be a simple graph on $n$ vertices and $J_G$ denote the corresponding binomial edge ideal in $S = K[x_1, \ldots, x_n, y_1,\ldots, y_n].$ We prove that the Castelnuovo-Mumford regularity of $J_G$ is bounded above by $c(G)+1$ when $G$ is a quasi-block graph or semi-block graph. We give another proof of Saeedi Madani-Kiani regularity upper bound conjecture for chordal graphs. We obtain the regularity of binomial edge ideals of Jahangir graphs. Later, we establish a sufficient condition for Hibi-Matsuda conjecture to be true.

math.CO↗
arXiv2021

Regularity of parity binomial edge ideals

Let $G$ be a simple graph on $n$ vertices and $\mathcal{I}_G$ denotes parity binomial edge ideal of $G$ in the polynomial ring $S = \mathbb{K}[x_1,\ldots, x_n, y_1, \ldots, y_n].$ We obtain a lower bound for the regularity of parity binomial edge ideals of graphs. We then classify all graphs whose parity binomial edge ideals have regularity $3$. We classify graphs whose parity binomial edge ideals have pure resolution.

math.AC↗
arXiv2021

Divisors of Fourier coefficients of two newforms

For a pair of distinct non-CM newforms of weights at least 2, having rational integral Fourier coefficients $a_{1}(n)$ and $a_{2}(n)$, under GRH, we obtain an estimate for the set of primes $p$ such that $$ ω(a_1(p)-a_2(p)) \le [ 7k+{1}/{2}+k^{1/5}],$$ where $ω(n)$ denotes the number of distinct prime divisors of an integer $n$ and $k$ is the maximum of their weights. As an application, under GRH, we show that the number of primes giving congruences between two such newforms is bounded by $[7k+{1}/{2}+k^{1/5} ]$. We also obtain a multiplicity one result for newforms via congruences.

math.NT↗
arXiv2021

Open strange meson $K^\pm_1$ in hot and dense nuclear matter

Using the unification of the chiral SU(3) model and QCD sum rules, we deduce the in-medium properties of $K^\pm_1$ meson. Within the chiral SU(3) model, medium modified gluon and quark condensates are evaluated through their interactions with the scalar fields ($σ$, $ζ$, $δ$, and $χ$). These condensates are further used as input in the Borel transformed equations of QCD sum rules to evaluate the in-medium mass of strange $K^\pm_1$ meson. The in-medium property of the above meson can be used to study the restoration of chiral symmetry in nuclear matter.

hep-ph↗
arXiv2021

Symbolic powers of certain cover ideals of graphs

In this paper, we compute the regularity and Hilbert series of symbolic powers of the cover ideal of a graph $G$ when $G$ is either a crown graph or a complete multipartite graph. We also compute the multiplicity of symbolic powers of cover ideals in terms of the number of edges.

math.AC↗
arXiv2021

$η$ mesons in hot magnetized nuclear matter

The $ηN$ interactions are investigated in the hot magnetized asymmetric nuclear matter using chiral SU(3) model and chiral perturbation theory (ChPT). In the chiral model, the in-medium properties of $η$-meson are calculated by the medium modified scalar densities under the influence of an external magnetic field. Further, in the combined approach of chiral model and ChPT, off-shell contributions of $ηN$ interactions are evaluated from the ChPT effective $ηN$ Lagrangian, and the in-medium effect of scalar densities are incorporated from the chiral SU(3) model. We observe a significant effect of magnetic field on the in-medium mass and optical potential of $η$ meson. We observe a deeper mass-shift in the combined approach of ChPT and chiral model compared to the effect of solo chiral SU(3) model. In both approaches, no additional mass-shift is observed due to the uncharged nature of $η$ mesons in the presence of magnetic field.

nucl-th↗