Browsing Mathematics by Title

Browsing Mathematics by Title

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  • Gupta, Rajat; Pandit, Sudip (Cornell University Library, 2021-06)
    The main aim of this paper is to study an analogue of the generalized divisor function in a number field K, namely, ?K,?(n). The Dirichlet series associated to this function is ?K(s)?K(s ??). We give an expression for the ...
  • 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 ...
  • Dixit, Atul; Kim, Sun; Zaharescu, Alexandru (American Mathematical Society, 2017-04)
    Let $ r_k(n)$ denote the number of representations of the positive integer $ n$ as the sum of $ k$ squares. In 1934, the Russian mathematician A. I. Popov stated, but did not rigorously prove, a beautiful series transformation ...
  • Dixit, Atul; Kim, Sun; Zaharescu, Alexandru; Berndt, Bruce C. (American Mathematical Society, 2017)
  • Dixit, Atul; Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru (Cornell University Library, 2016-10)
    Let rk(n) denote the number of representations of the positive integer n as the sum of k squares. In 1934, the Russian mathematician A. I. Popov stated, but did not rigorously prove, a beautiful series transformation ...
  • Tyagi, Jagmohan (Taylor & Francis, 2013-06)
    In this note, we discuss an eigenvalue problem involving Hardy's potential with homogeneous Dirichlet boundary condition in a smooth bounded domain. We show that the problem possesses a continuous family of eigenvalues.
  • Kour, Surjeet; Vishakha (Cornell University Library, 2015-05)
    Let G=H×A be a finite group, where H is a purely non-abelian subgroup of G and A is a non-trivial abelian factor of G. Then, for n≥2, we show that there exists an isomorphism ϕ:Autγn(G)Z(G)(G)→Autγn(H)Z(H)(H) such that ...
  • Sharma, Vishakha; Kour, Surjeet (Taylor & Francis, 2017-02)
    Let G = H×A be a group, where H is a purely non-Abelian subgroup of G, and A is a non-trivial Abelian factor of G. Then, for n≥2, we show that there exists an isomorphism ϕ:Autγn(G)Z(G)(G)→Autγn(H)Z(H)(H) such that ...
  • Amrutiya, Sanjay (Springer International Publishing, 2016-03)
    In this article, we prove that the Faltings theta functions on moduli of parabolic bundles over a smooth projective curve can be used to give an explicit scheme-theoretic projective embedding.
  • Vatwani, Akshaa; Wong, Peng-Jie (Instytut Matematyczny, 2020)
  • Dixit, Atul; Kumar, Rahul (World Scientific Publishing, 2020-06)
  • Dixit, Atul; Kumar, Rahul (Cornell University Library, 2019-12)
    We obtain a new proof of Hurwitz's formula for the Hurwitz zeta function ?(s,a) beginning with Hermite's formula. The aim is to reveal a nice connection between ?(s,a) and a special case of the Lommel function S?,?(z). ...
  • Kour, Surjeet (Cornell University Library, 2017-01)
    Let G be a finite group and M,N be two normal subgroups of G. Let AutMN(G) denote the group of all automorphisms of G which fix N element wise and act trivially on G/M. Let n be a positive integer. In this article we have ...
  • Bhardwaj, Om Prakash; Goel, Kriti; Sengupta, Indranath (Cornell University Library, 2021-05)
    Let H be a numerical semigroup minimally generated by an almost arithmetic sequence. We give a complete description of the row-factorization (RF) matrices associated with the pseudo-Frobenius elements of H. RF-matrices ...
  • Dhara, Anulekha; Luc, Dinh The; Tinh, Phan Nhat (Springer Verlag, 2012)
    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 ...
  • Gupta, Rajat; Kumar, Rahul (Cornell University Library, 2020-12)
    n this article, a q-series examined by Kluyver and Uchimura is generalized. This allows us to find generalization of the identities in the random acyclic digraph studied by Simon, Crippa, and Collenberg in 1993. As one of ...
  • Gupta, Rajat; Kumar, Rahul (Elsevier, 2021-11)
    In this article, a q-series examined by Kluyver and Uchimura is generalized. This allows us to find generalization of the identities in the random acyclic digraph studied by Simon, Crippa, and Collenberg in 1993. As one ...
  • 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 . ...
  • Gupta, Rajat (Cornell University, 2020-02)
  • Gupta, Rajat (Elsevier, 2021-11)
    In this article, a finite analogue of the generalized sum-of-tails identity of Andrews and Freitas is obtained. We derive several interesting results as special cases of this analogue, in particular, a recent identity of ...

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