We consider a certain class of multiplicative functions f:N→C. Let F(s)=∑∞n=1f(n)n−s be the associated Dirichlet series and FN(s)=∑n≤Nf(n)n−s be the truncated Dirichlet series. In this setting, we obtain new Hal\'asz-type ...
Quasilocal formulations of black hole are of immense importance since they reveal the essential and minimal assumptions required for a consistent description of black hole horizon, without relying on the asymptotic boundary ...
In this paper we compute Gr�bner bases for determinantal ideals of the form , where X and Y are both matrices whose entries are indeterminates over a field K. We use the Gr�bner basis structure to determine Betti numbers ...
Dixit, Atul; Maji, Bibekananda(Cornell University Library, 2018-06)
A generalization of a beautiful q-series identity found in the unorganized portion of Ramanujan's second and third notebooks is obtained. As a consequence, we derive a new three-parameter identity which is a rich source ...
In 1914, Hardy proved that infinitely many non-trivial zeros of the Riemann zeta function lie on the critical line using the transformation formula of the Jacobi theta function. Recently the first author obtained an integral ...
Mehta, Ranjana; Saha, Joydip; Sengupta, Indranath(Cornell University Library, 2018-05)
Given integer e?4, we have constructed a class of symmetric numerical semigroups of embedding dimension e and proved that the cardinality of a minimal presentation of the semigroup is a bounded function of the embedding ...
We address the parameterized complexity of Max Colorable Induced Subgraph on perfect graphs. The problem asks for a maximum sized q-colorable induced subgraph of an input graph G. Yannakakis and Gavril (Inf Process Lett ...
In this note, we discuss the isolatedness, simplicity and nodal estimate for the first eigenvalue of fractional Laplacian of Kirchhoff type. This work is motivated by the recent works on the fractional eigenvalues.
A network of sensors observes a time-inhomo-geneous Poisson signal and within a fixed time interval has to decide between two hypotheses regarding the signal’s intensity. The paper reveals an interplay between network ...
Mehta, Ranjana; Saha, Joydip; Sengupta, Indranath(Cornell University Library, 2018-02)
Suppose e≥4 be an integer, a=e+1, b>a+(e−3)d, gcd(a,d)=1 and d∤(b−a). Let M={a,a+d,a+2d,…,a+(e−3)d,b,b+d}, which forms a minimal generating set for the numerical semigroup Γe(M), generated by the set M. We calculate the ...
The Abel-Tauber process consists of the Abelian process of forming the Riesz sums and the subsequent Tauberian process of differencing the Riesz sums, an analogue of the integration-differentiation process. In this article, ...
A comprehensive study of the generalized Lambert series ∑n=1∞nN−2hexp(−anNx)1−exp(−nNx),0<a≤1, x>0, N∈N and h∈Z, is undertaken. Two of the general transformations of this series that we obtain here lead to two-parameter ...
We show that every problem in the complexity class (Statistical Zero Knowledge) is efficiently reducible to the Minimum Circuit Size Problem (). In particular Graph Isomorphism lies in .
This is the first theorem ...
Mehta, Ranjana; Saha, Joydip; Sengupta, Indranath(Cornell University Library, 2018-01)
Bresinsky defined a class of monomial curves in A4 with the property that the minimal number of generators or the first Betti number of the defining ideal is unbounded above. We prove that the same behaviour of unboundedness ...