Journal Articleshttps://repository.iitgn.ac.in/handle/123456789/5522019-08-23T01:35:51Z2019-08-23T01:35:51ZOn squares of odd zeta values and analogues of Eisenstein seriesDixit, AtulGupta, Rajathttps://repository.iitgn.ac.in/handle/123456789/46042019-07-16T09:58:27Z2019-06-01T00:00:00ZOn squares of odd zeta values and analogues of Eisenstein series
Dixit, Atul; Gupta, Rajat
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 . The formula for is then generalized in two different directions, one, by considering the generalized divisor function , and the other, by studying a more general analogue of the aforementioned Eisenstein series, consisting of one more parameter N. A number of important special cases are derived from the first generalization. For example, we obtain a series representation for , where ? is a non-trivial zero of . We also evaluate a series involving the modified Bessel function of the second kind in the form of a rational linear combination of and for .
2019-06-01T00:00:00ZPrimary decomposition and normality of certain determinantal idealsSaha, JoydipSengupta, IndranathTripathi, Gaurabhttps://repository.iitgn.ac.in/handle/123456789/45962019-07-16T09:58:26Z2019-06-01T00:00:00ZPrimary decomposition and normality of certain determinantal ideals
Saha, Joydip; Sengupta, Indranath; Tripathi, Gaurab
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.
2019-06-01T00:00:00ZSemilinear elliptic problems with singular terms on the Heisenberg groupKumar, Dharmendrahttps://repository.iitgn.ac.in/handle/123456789/45762019-06-29T06:04:57Z2019-05-01T00:00:00ZSemilinear elliptic problems with singular terms on the Heisenberg group
Kumar, Dharmendra
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 exists a solution u?H01(?,Hn) ?L?(?) to this problem. The interesting point of the problem under consideration is that it has a strong singularity.
2019-05-01T00:00:00ZGelfand-Kirillov dimension of the quantized algebra of regular functions on homogeneous spacesChakraborty, Partha SarathiSaurabh, Bipulhttps://repository.iitgn.ac.in/handle/123456789/45292019-06-19T11:12:57Z2019-05-01T00:00:00ZGelfand-Kirillov dimension of the quantized algebra of regular functions on homogeneous spaces
Chakraborty, Partha Sarathi; Saurabh, Bipul
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 a real differentiable manifold.
2019-05-01T00:00:00Z