• On squares of odd zeta values and analogues of Eisenstein series 

  Dixit, Atul; Gupta, Rajat (Elsevier, 2019-06)

  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 . ...
• Primary decomposition and normality of certain determinantal ideals 

  Saha, Joydip; Sengupta, Indranath; Tripathi, Gaurab (Springer, 2019-06)

  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.
• Semilinear elliptic problems with singular terms on the Heisenberg group 

  Kumar, Dharmendra (Taylor & Francis, 2019-05)

  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 ...
• Gelfand-Kirillov dimension of the quantized algebra of regular functions on homogeneous spaces 

  Chakraborty, Partha Sarathi; Saurabh, Bipul (American Mathematical Society, 2019-05)

  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 ...
• Positive solution to extremal Pucci's equations with singular and gradient nonlinearity 

  Tyagi, Jagmohan; Verma, Ram Baran (American Institute of Mathematical Sciences, 2019)
• Generalized Lambert series and arithmetic nature of odd zeta values 

  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 ...
• Stability of positive solution to fractional logistic equations 

  Dwivedi, Gaurav; Tyagi, Jagmohan; Verma, Ram Baran (Japana Matematika Societo, 2019-04)
• Sparse reconstruction of log-conductivity in current density impedance tomography 

  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 ...
• A simple proof of a congruence for a series involving the little q-Jacobi polynomials 

  Dixit, Atul (Cornell University Library, 2019-02)
• Zeros of partial sums of L-functions 

  Roy, Arindam; Vatwani, Akshaa (Elsevier, 2019-04)
• Studies on the existence of positive viscosity solutions to fully nonlinear elliptic PDEs 

  Verma, Ram Baran (Indian Institute of Technology Gandhinagar, 2018)
• Transversal intersection of monomial ideals 

  Saha, Joydip; Sengupta, Indranath; Tripathi, Gaurab (Indian Academy of Science, 2018-12)
• Semilinear elliptic problems with singular terms on the Heisenberg group 

  Kumar, Dharmendra (Taylor & Francis, 2018-12)
• Untrodden pathways in the theory of the restricted partition function p(n,N 

  Dixit, Atul; Eyyunni, Pramod; Maji, Bibekananda; Sood, Garima (Cornell University Library, 2018-12)
• Quiver representations and their applications 

  Amrutiya, Sanjay (SCIELO, 2018-12)

  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.
• Sturm-Picone theorem for fractional nonlocal equations 

  Tyagi, Jagmohan (Cornell University Library, 2018-11)
• A note on certain Tannakian group schemes 

  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. ...
• A note on Leighton's variational lemma for fractional laplace equations 

  Tyagi, Jagmohan (European Mathematical Society (EMS), 2018-10)

  In this note, we establish Leighton's variational lemma for fractional Laplace equations. We use the classical techniques to establish this variational lemma. We also point out several questions concerning the zeros of the ...
• The generalized modified Bessel function Kz,w(x) at z=1/2 and Humbert functions, 

  Kumar, Rahul (Cornell University Library, 2018-10)

  Recently Dixit, Kesarwani, and Moll introduced a generalization Kz,w(x) of the modified Bessel function Kz(x) and showed that it satisfies an elegant theory similar to Kz(x). In this paper, we show that while K12(x) is an ...
• Modular-type transformations and integrals involving the Riemann ?-function 

  Dixit, Atul (Indian Mathematical Society, 2018-09)

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