Journal Articles
https://repository.iitgn.ac.in/handle/123456789/552
2019-03-24T01:40:43ZZeros of partial sums of L-functions
https://repository.iitgn.ac.in/handle/123456789/4270
Zeros of partial sums of L-functions
Roy, Arindam; Vatwani, Akshaa
We consider a certain class of multiplicative functions�f:N?C. Let�F(s)=?n=1?f(n)n?s�be the associated�Dirichlet series�and�FN(s)=?n?Nf(n)n?sbe the truncated Dirichlet series. In this setting, we obtain new Hal�sz-type results for the logarithmic mean value of�f. More precisely, we prove estimates for the sum�?n=1xf(n)/n�in terms of the size of�|F(1+1/log?x)|�and show that these estimates are sharp. As a consequence of our mean value estimates, we establish non-trivial zero-free regions for the partial sums�FN(s).In particular, we study the zero distribution of partial sums of the Dedekind�zeta function�of a number field�K. More precisely, we give some improved results for the number of zeros up to height�T�as well as new zero density results for the number of zeros up to height�T, lying to the right of�Re(s)=?, where�??1/2.
2019-04-01T00:00:00ZTransversal intersection of monomial ideals
https://repository.iitgn.ac.in/handle/123456789/4057
Transversal intersection of monomial ideals
Saha, Joydip; Sengupta, Indranath; Tripathi, Gaurab
2018-12-01T00:00:00ZSemilinear elliptic problems with singular terms on the Heisenberg group
https://repository.iitgn.ac.in/handle/123456789/4054
Semilinear elliptic problems with singular terms on the Heisenberg group
Kumar, Dharmendra
2018-12-01T00:00:00ZQuiver representations and their applications
https://repository.iitgn.ac.in/handle/123456789/4027
Quiver representations and their applications
Amrutiya, Sanjay
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.
2018-12-01T00:00:00Z