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  • 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; Roy, Arindam; Zaharescu, Alexandru (Elsevier, 2016-03)
    We give character analogues of a generalization of a result due to Ramanujan, Hardy and Littlewood, and provide Riesz-type criteria for Riemann Hypotheses for the Riemann zeta function and Dirichlet L-functions. We also ...
  • Berndt, Bruce C.; Dixit, Atul; Kim, Sun; Zaharescu, Alexandru (Elsevier, 2018-11)
    Letrk(n) denote the number of representations of the positive integernas thesum ofksquares. We rigorously prove for the first time a Vorono ?? summation formula forrk(n), k?2,proved incorrectly by A. I. Popov and later ...

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