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  • 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. ...
  • 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    In his unpublished manuscript on the partition and tau functions, Ramanujan obtained several striking congruences for the partition function p(n), the number of unrestricted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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • Dhama, Shivam; Pahlajani, Chetan D. (American Institute of Mathematical Sciences (AIMS), 2022-04)
    In this paper, we study the dynamics of a linear control system with given state feedback control law in the presence of fast periodic sampling at temporal frequency $ 1/\delta $ ($ 0 < \delta \II 1 $), together with small ...

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