Dixit, Atul; Kumar, Rahul(Cornell University Library, 2019-12)
We obtain a new proof of Hurwitz's formula for the Hurwitz zeta function ?(s,a) beginning with Hermite's formula. The aim is to reveal a nice connection between ?(s,a) and a special case of the Lommel function S?,?(z). ...
We give a simple and a more explicit proof of a mod 4 congruence for a series involving the little q-Jacobi polynomials which arose in a recent study of a certain restricted overpartition function.
Saha, Joydip; Sengupta, Indranath(Cornell University Library, 2019-09)
In this paper we explicitly compute the derivation module of quotients of polynomial rings by ideals formed by the sum or by some other gluing technique. We discuss cases of monomial ideals and binomial ideals separately.
A Ramanujan-type formula involving the squares of odd zeta values is obtained. The crucial part in obtaining such a result is to conceive the correct analogue of the Eisenstein series involved in Ramanujan's formula for . ...
In this paper, we study primality and primary decomposition of certain ideals which are generated by homogeneous degree 2 polynomials and occur naturally from determinantal conditions. Normality is derived from these results.
We consider the semilinear elliptic problem: ??Hnu??g(?)u(|z|4+t2)1/2=?f(?)u?+h(?)upin ?,u>0in ?,u=0on ??. where ??Hn is an open bounded subset, N?3;0??,0?f,g,h?L?(?). Under assumptions ?,p>0,?>0 small we show that there ...
In this article, we prove that the Gelfand-Kirillov dimension of the quantized algebra of regular functions on certain homogeneous spaces of types $ A$, $ C$, and $ D$ is equal to the dimension of the homogeneous space as ...
Dixit, Atul; Maji, Bibekananda(Cambridge University Press, 2019-02)
It is pointed out that the generalized Lambert series��studied by Kanemitsu, Tanigawa and Yoshimoto can be found on page 332 of Ramanujan's Lost Notebook in a slightly more general form. We extend an important transformation ...
Gupta, Madhu; Mishra, Rohit Kumar; Roy, Souvik(Cornell University Library, 2019-03)
A new non-linear optimization approach is proposed for the sparse reconstruction of log-conductivities in current density impedance imaging. This framework comprises of minimizing an objective functional involving a least ...
In this article, we survey some results on geometric methods to study quiver representations, and applications of these results to sheaves, equivariant sheaves and parabolic bundles.
Amrutiya, Sanjay(Cornell University Library, 2018-10)
In this note, we prove that the F-fundamental group scheme is birational invariant for smooth projective varieties. We prove that the F-fundamental group scheme is naturally a quotient of the Nori fundamental group scheme. ...