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Divyum Sharma

Assistant Professor, Department of Mathematics,
BITS Pilani, Pilani Campus

Number Theory
Office: 6165B,
Department of Mathematics, Birla Institute of Technology & Science, Pilani- 333031, Rajasthan. India.

Publications

  • On the representation of an integer in Ostrowski and recurrence numeration systems (with Mohit Mittal), https://arxiv.org/abs/2409.06232, submitted.

  • On the representation of an imaginary quadratic integer in two different bases, https://arxiv.org/abs/2311.17348, accepted for publication in Publ. Math. Debrecen.

  • Diagonalizable Thue Equations -- revisited (with N. Saradha), http://arxiv.org/abs/2204.12082, Ramanujan J. (2023) 62, 291–306.
  • Rational solutions to the variants of Erdos-Selfridge superelliptic curves (with P. Das, S. Laishram, N. Saradha), https://arxiv.org/abs/2105.02792, Int. J. Number Theory (2023) 19–07, 1707–1744.
  • On the coefficient-choosing game (with L. Singhal), Moscow J. of Combinatorics and Number Theory 10--3 (2021), 183--202.
  • Joint distribution in residue classes of the base-$q$ and Ostrowski digital sumsUnif. Distrib. Theory 14 (2019), no. 2, 1-26.
  • Thue's inequalities and the hypergeometric method (with S. Akhtari and N. Saradha), Ramanujan J. 45 (2018), no. 2, 521-567.
  • A note on Thue inequalities with few coefficients (with N. Saradha), Alladi60: Analytic Number Theory, Modular Forms and q-Hypergeometric Series, Springer Proc. Math. Stat., 221, Springer, Cham (2017), 665-675.
  • Contributions to a conjecture of Mueller and Schmidt on Thue inequalities (with N. Saradha), Proceedings - Mathematical Sciences 127 (2017), no. 4, 565-584.
  • On the number of non-zero digits of integers in multi-base representations (with Cs. Bertok, L. Hajdu and F. Luca), Publ. Math. Debrecen (2017) 90/1-2, 181-194.
  • Number of solutions of cubic Thue inequalities with positive discriminant (with N. Saradha), Acta Arith. 171 (2015), no. 1, 81-95.
  • Simultaneous rational approximation via Rickert's Integrals  (with N. Saradha), Indag. Math. (N. S.) 26 (2015), 88-105.
  • Arithmetic nature of infinite series and integrals (with N. Saradha), Contemp. Math. (2015) 655, 191-207.
  • Number of representations of integers by binary forms (with N. Saradha), Publ. Math. Debrecen 85/1-2 (2014); Corrigendum ibid. 86/3-4 (2015), 503-504.