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Distribution of Residues Modulo p Using the Dirichlet’s Class Number Formula

In: Class Groups of Number Fields and Related Topics

Author

Listed:
  • Jaitra Chattopadhyay

    (Harish-Chandra Research Institute, HBNI)

  • Bidisha Roy

    (Harish-Chandra Research Institute, HBNI)

  • Subha Sarkar

    (Harish-Chandra Research Institute, HBNI)

  • R. Thangadurai

    (Harish-Chandra Research Institute, HBNI)

Abstract

Let p be an odd prime number. In this article, we study the number of quadratic residues and non-residues modulo p which are multiples of 2 or 3 or 4 and lying in the interval $$[1, p-1]$$, by applying the Dirichlet’s class number formula for the imaginary quadratic field $$\mathbb {Q}(\sqrt{-p})$$.

Suggested Citation

  • Jaitra Chattopadhyay & Bidisha Roy & Subha Sarkar & R. Thangadurai, 2020. "Distribution of Residues Modulo p Using the Dirichlet’s Class Number Formula," Springer Books, in: Kalyan Chakraborty & Azizul Hoque & Prem Prakash Pandey (ed.), Class Groups of Number Fields and Related Topics, pages 97-107, Springer.
    • Handle: RePEc:spr:sprchp:978-981-15-1514-9_9
    DOI: 10.1007/978-981-15-1514-9_9
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