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Mathematics: Recent submissions

  • Extended higher Herglotz function \textup{II} 
    Gupta, Rajat; Kumar, Rahul (Cornell University Library, 2022-04)
    Very recently, Radchenko and Zagier revived the theory of Herglotz functions. The main goal of the article is to show that one of the formulas on page 220 of Ramanujan's Lost Notebook actually lives in the realms of this ...
  • Asymptotics and sign patterns for coefficients in expansions of Habiro elements 
    Goswami, Ankush; Jha, Abhash Kumar; Kim, Byungchan; Osburn, Robert (Cornell University Library, 2022-04)
    We prove asymptotics and study sign patterns for coefficients in expansions of elements in the Habiro ring which satisfy a strange identity. As an application, we prove asymptotics and discuss positivity for the generalized ...
  • The generalized Saint Venant operator and integral moment transforms 
    Mishra, Rohit Kumar; Sahoo, Suman Kumar (Cornell University Library, 2022-03)
    In this article, we work with a generalized Saint Venant operator introduced by Vladimir Sharafutdinov to describe the kernel of the integral moment transforms over symmetric m-tensor fields in n-dimensional Euclidean ...
  • The C∞-isomorphism property for a class of singularly-weighted X-ray transforms 
    Mishra, Rohit Kumar; Monard, Francois; Zou, Yuzhou (Cornell University Library, 2022-03)
    We study various self-adjoint realizations of the X-ray transform on the Euclidean disk D, obtained by considering specific singularly weighted L2 topologies. We first recover the well-known Singular Value Decompositions ...
  • Cohen-macaulay binomial edge ideals in terms of blocks with whiskers 
    Saha, Kamalesh; Sengupta, Indranath (Cornell University Library, 2022-03)
    For a graph G, Bolognini et al. have shown JG is strongly unmixed ? JG is Cohen-Macaulay ? G is accessible, where JG denotes the binomial edge ideals of G. Accessible and strongly unmixed properties are purely combinatorial. ...
  • Derivation modules for sum and gluing 
    Saha, Joydip; Sengupta, Indranath (Indian Academy of Sciences, 2022-06)
    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.
  • Unboundedness of the first and the last Betti numbers of numerical semigroups segnerated by concatenation 
    Mehta, Ranjana; Saha, Joydip; Sengupta, Indranath (Cornell University Library, 2022-02)
    We show that the minimal number of generators and the Cohen-Macaulay type of a family of numerical semigroups generated by concatenation of arithmetic sequences is unbounded.
  • A gauge theoretic aspects of parabolic bundles over Klein surfaces 
    Amrutiya, Sanjay; Jaiswal, Ayush (Cornell University Library, 2022-02)
    In this article, we study the gauge theoretic aspects of real and quaternionic parabolic bundles over a real curve (X,?X), where X is a compact Riemann surface and {\sigma}X is an anti-holomorphic involution. For a fixed ...
  • Asymptotic analysis of discrete-time models for linear control systems with fast random sampling 
    Dhama, Shivam; Pahlajani, Chetan D. (2021-12-20)
  • On a conjecture of sun about sums of restricted squares 
    Banerjee, Soumyarup (Cornell University Library, 2022-02)
    In this paper, we investigate sums of four squares of integers whose prime factorizations are restricted, making progress towards a conjecture of Sun that states that two of the integers may be restricted to the forms 2a3b ...
  • The relationship of the Gaussian curvature with the curvature of a Cowen-Douglas operator 
    Ghara, Soumitra; Misra, Gadadhar (Cornell University Library, 2022-02)
    It has been recently shown that if K is a sesqui-analytic scalar valued non-negative definite kernel on a domain Ω in Cm, then the function (K2∂i∂¯jlogK)mi,j=1, is also a non-negative definite kernel on Ω. In this paper, ...
  • Commuting tuple of multiplication operators homogeneous under the unitary group 
    Ghara, Soumitra; Kumar, Surjit; Misra, Gadadhar; Pramanick, Paramita (Cornell University Library, 2022-01)
    Let Bd be the open Euclidean ball in Cd and T:=(T1,…,Td) be a commuting tuple of bounded linear operators on a complex separable Hilbert space H. Let U(d) be the linear group of unitary transformations acting on Cd by the ...
  • Combinatorial identities associated with a bivariate generating function for overpartition pairs 
    Dixit, Atul; Goswami, Ankush (Cornell University Library, 2022-01)
    We obtain a three-parameter q-series identity that generalizes two results of Chan and Mao. By specializing our identity, we derive new results of combinatorial significance in connection with N(r,s,m,n), a function counting ...
  • A homogenised model for flow, transport and sorption in a heterogeneous porous medium 
    Auton, Lucy C.; Pramanik, Satyajit; Dalwadi, Mohit P.; MacMinn, Christopher W.; Griffiths, Ian M. (Cambridge University Press., 2022-02)
    A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory ...
  • Equivalent criterion for the grand Riemann hypothesis associated to Maass cusp forms 
    Banerjee, Soumyarup; Kumar, Rahul (Cornell University, 2021-12)
    In this article, we obtain transformation formulas analogous to the identity of Ramanujan, Hardy and Littlewood in the setting of primitive Maass cusp form over the congruence subgroup Γ0(N) and also provide an equivalent ...
  • Ramanujan and Koshliakov meet Abel and Plana 
    Berndt, Bruce C.; Dixit, Atul; Gupta, Rajat; Zaharescu, Alexandru (Cornell University, 2021-12)
    The neglected Russian mathematician, N.~S.~Koshliakov, derived beautiful generalizations of the classical Abel--Plana summation formula through a setting arising from a boundary value problem in heat conduction. When we ...
  • Affine semigroups of maximal projective dimension 
    Goel, Kriti (09-01-22)
  • Some identities for the partition function 
    Goswami, Ankush; Jha, Abhash Kumar; Singh, Anup Kumar (Elsevier, 2022-04)
    In his unpublished manuscript on the partition and tau functions, Ramanujan obtained several striking congruences for the partition function p(n), the number of unrestricted partitions of n. The most notable of them are ...
  • The v-number of monomial ideals 
    Saha, Kamalesh; Sengupta, Indranath (Cornell University Library, 2021-11)
    We generalize some results of v-number for arbitrary monomial ideals by showing that the v-number of an arbitrary monomial ideal is the same as the v-number of its polarization. We prove that the v-number v(I(G)) of the ...
  • Projective closure of gluing of affine monomial curves 
    Saha, Joydip; Sengupta, Indranath; Srivastava, Pranja (Cornell University Library, 2021-11)
    Our aim in this paper is to study the arithmetically Cohen-Macaulay and the Gorenstein properties of the projective closure of an affine monomial curve obtained by gluing two affine monomial curves. We introduce the notion ...

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