• Fluctuation analysis for a class of nonlinear systems with fast periodic sampling and small state-dependent white noise 

  Dhama, Shivam; Pahlajani, Chetan D. (Cornell University Library, 2022-05)

  We consider a nonlinear differential equation under the combined influence of small state-dependent Brownian perturbations of size ε, and fast periodic sampling with period δ; 0<ε,δ≪1. Thus, state samples (measurements) ...
• Lambert series of logarithm, the derivative of deninger's function R(z) and a mean value theorem for ζ(12−it) ζ′(12+it) 

  Banerjee, Soumyarup; Dixit, Atul; Gupta, Shivajee (Cornell University Library, 2022-05)

  An explicit transformation for the series ∑n=1∞log(n)eny−1, Re(y)>0, which takes y to 1/y, is obtained for the first time. This series transforms into a series containing ψ1(z), the derivative of Deninger's function R(z). ...
• Kernel of arithmetic jet spaces 

  Saha, Arnab (Cornell University Library, 2022-04)

  Fix a Dedekind domain O and a non-zero prime p in it along with a uniformizer π. In the first part of the paper, we construct m-shifted π-typical Witt vectors Wmn(B) for any O algebra B of length m+n+1. They are a ...
• Two general series identities involving modified bessel functions and a class of arithmetical functions 

  Berndt, Bruce C.; Dixit, Atul; Gupta, Rajat; Zaharescu, Alexandru (Cornell University Library, 2022-04)

  We consider two sequences a(n) and b(n), 1≤n<∞, generated by Dirichlet series ∑n=1∞a(n)λsnand∑n=1∞b(n)μsn,satisfying a familiar functional equation involving the gamma function Γ(s). Two general identities are established. ...
• 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 ...
• 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 ...
• 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. ...
• 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 ...
• 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 ...
• 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 ...
• 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 ...
• 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 ...
• Affine semigroups of maximal projective dimension 

  Bhardwaj, Om Prakash; Goel, Kriti; Sengupta, Indranath (Cornell University Library, 2021-11)

  We generalize the notion of symmetric semigroups, pseudo symmetric semigroups, and row factorization matrices for pseudo Frobenius elements of numerical semigroups to the case of semigroups with maximal projective dimension ...

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