arXiv subjects

Arindam Roy

Publications and source records attributed to Arindam Roy.

25 records · Page 2Linked to original sources

arXiv2016

Long Term Performance Studies of Large Oil-Free Bakelite Resistive Plate Chamber

Several high energy physics and neutrino physics experiments worldwide require large-size RPCs to cover wide acceptances. The muon tracking systems in the Iron calorimeter (ICAL) in the INO experiment, India and the near detector in DUNE at Fermilab are two such examples. A (240 cm $\times$ 120 cm $\times$ 0.2 cm) bakelite RPC has been built and tested at Variable Energy Cyclotron Centre, Kolkata, using indigenous materials procured from the local market. No additional lubricant, like oil has been used on the electrode surfaces for smoothening. The chamber is in operation for $>$ 365 days. We have tested the chamber for its long term operation. The leakage current, bulk resistivity, efficiency, noise rate and time resolution of the chamber have been found to be quite stable during the testing peroid. It showed an efficiency $>$ 95$\%$ with an average time resolution of $\sim$0.83 ns at the point of measurement at 9000 V throughout the testing period. Details of the long term performance of the chamber have been discussed.

physics.ins-det↗

arXiv2015

Moments of averages of generalized Ramanujan sums

Let $β$ be a positive integer. A generalization of the Ramanujan sum due to Cohen is given by \begin{align} c_{q,β}(n) := \sum\limits_{{{(h,{q^β})}_β} = 1} {e^{2πinh/{q^β}}}, \nonumber \end{align} where $h$ ranges over the the non-negative integers less than $q^β$ such that $h$ and $q^β$ have no common $β$-th power divisors other than $1$. The distribution of the average value of the Ramanujan sum is a subject of extensive research. In this paper, we study the distribution of the average value of $c_{q,β}(n)$ by computing the $k$-th moments of the average value of $c_{q,β}(n)$. In particular we have provided the first and second moments with improved error terms. We give more accurate results for the main terms than our predecessors. We also provide an asymptotic result for an extension of a divisor problem and for an extension of Ramanujan's formula.

math.NT↗

arXiv2015

Koshliakov kernel and identities involving the Riemann zeta function

Some integral identities involving the Riemann zeta function and functions reciprocal in a kernel involving the Bessel functions $J_{z}(x), Y_{z}(x)$ and $K_{z}(x)$ are studied. Interesting special cases of these identities are derived, one of which is connected to a well-known transformation due to Ramanujan, and Guinand.

math.NT↗

arXiv2013

Zeros of partial sums of the Dedekind zeta function of a cyclotomic field

In this article, we study the zeros of the partial sums of the Dedekind zeta function of a cyclotomic field $K$ defined by the truncated Dirichlet series \[ ζ_{K, X} (s) = \sum_{\|\mathfrak{a}\| \leq X} \frac{1}{\|\mathfrak{a}\|^{s}}, \] where the sum is to be taken over nonzero integral ideals $\mathfrak{a}$ of $K$ and $\|\mathfrak{a}\|$ denotes the absolute norm of $\mathfrak{a}$. Specifically, we establish the zero-free regions for $ζ_{K, X} (s)$ and estimate the number of zeros of $ζ_{K, X} (s)$ up to height $T$.

math.NT↗

arXiv2013

Monotonicity Results for Dirichlet L-functions

We present some monotonicity results for Dirichlet $L$-functions associated to real primitive characters. We show in particular that these Dirichlet $L$-functions are far from being logarithmically completely monotonic. Also, we show that, unlike in the case of the Riemann zeta function, the problem of comparing the signs of $\frac{d^k}{ds^k}\log L(s,χ)$ at any two points $s_1, s_2>1$ is more subtle.

math.NT↗

arXiv2011

Convexity of Quotients of Theta Functions

For fixed $u$ and $v$ such that $0\leq u<v<1/2$, the monotonicity of the quotients of Jacobi theta functions, namely, $θ_{j}(u|iπt)/θ_{j}(v|iπt)$, $j=1, 2, 3, 4$, on $0<t<\infty$ has been established in the previous works of A.Yu. Solynin, K. Schiefermayr, and Solynin and the first author. In the present paper, we show that the quotients $θ_{2}(u|iπt)/θ_{2}(v|iπt)$ and $θ_{3}(u|iπt)/θ_{3}(v|iπt)$ are convex on $0<t<\infty$.

math.CA↗

arXiv2011

Sums of magnetic eigenvalues are maximal on rotationally symmetric domains

The sum of the first n energy levels of the planar Laplacian with constant magnetic field of given total flux is shown to be maximal among triangles for the equilateral triangle, under normalization of the ratio (moment of inertia)/(area)^3 on the domain. The result holds for both Dirichlet and Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary conditions too. The square similarly maximizes the eigenvalue sum among parallelograms, and the disk maximizes among ellipses. More generally, a domain with rotational symmetry will maximize the magnetic eigenvalue sum among all linear images of that domain. These results are new even for the ground state energy (n=1).

math.AP↗