Mathematicshttp://repository.iitgn.ac.in/handle/123456789/5472018-01-24T01:52:56Z2018-01-24T01:52:56ZZeros of combinations of the Riemann ?-function and the confluent hypergeometric function on bounded vertical shiftsDixit, AtulKumar, RahulMaji, BibekanandaZaharescu, Alexandruhttp://repository.iitgn.ac.in/handle/123456789/33592018-01-08T12:33:50Z2017-12-01T00:00:00ZZeros of combinations of the Riemann ?-function and the confluent hypergeometric function on bounded vertical shifts
Dixit, Atul; Kumar, Rahul; Maji, Bibekananda; Zaharescu, Alexandru
2017-12-01T00:00:00ZQuadrics defined by skew-symmetric matricesSaha, JoydipSengupta, IndranathTripathi, Gaurabhttp://repository.iitgn.ac.in/handle/123456789/33382017-12-06T05:29:08Z2017-11-01T00:00:00ZQuadrics defined by skew-symmetric matrices
Saha, Joydip; Sengupta, Indranath; Tripathi, Gaurab
In this paper we propose a model for computing a minimal free resolution for ideals of the form I1(XnYn), where Xn is an n n skew-symmetric matrix with indeterminate entries xij and Yn is a generic column matrix with indeterminate entries yj. We verify that the model works for n = 3 and n = 4 and pose some statements as conjectures. Answering the conjectures in a rmative would enable us to computea minimal free resolution for general n.
2017-11-01T00:00:00ZA generalized modified Bessel function and a higher level analogue of the theta transformation formulaDixit, AtulKesarwani, AashitaMoll, Victor H.http://repository.iitgn.ac.in/handle/123456789/33102017-12-06T05:29:05Z2017-10-01T00:00:00ZA generalized modified Bessel function and a higher level analogue of the theta transformation formula
Dixit, Atul; Kesarwani, Aashita; Moll, Victor H.
A new generalization of the modified Bessel function of the second kind is studied. Elegant series and integral representations, a differential-difference equation and asymptotic expansions are obtained for it thereby anticipating a rich theory that it may possess. The motivation behind introducing this generalization is to have a function which gives a new pair of functions reciprocal in the Koshliakov kernel and which subsumes the self-reciprocal pair involving . Its application towards finding modular-type transformations of the form , where , is given. As an example, we obtain a beautiful generalization of a famous formula of Ramanujan and Guinand equivalent to the functional equation of a non-holomorphic Eisenstein series on . This generalization can be considered as a higher level analogue of the general theta transformation formula. We then use it to evaluate an integral involving the Riemann ?-function and consisting of a sum of products of two confluent hypergeometric functions.
2017-10-01T00:00:00ZOn second-order conditions for nonsmooth problems with constraintsDhara, AnulekhaLuc, Dinh TheTinh, Phan Nhathttp://repository.iitgn.ac.in/handle/123456789/32622017-11-08T19:35:11Z2012-01-01T00:00:00ZOn second-order conditions for nonsmooth problems with constraints
Dhara, Anulekha; Luc, Dinh The; Tinh, Phan Nhat
To study the su ciency of an optimization problem, one either imposes
some convexity assumptions or consider second order optimality conditions. In this
paper we establish second order optimality conditions for nonsmooth optimization
problems by considering second order approximations of the functions involved and
by introducing the concept of second order tangentiability.
2012-01-01T00:00:00Z