ON SOME SYMMETRIES OF THE BASE n EXPANSION OF 1/m: THE CLASS NUMBER CONNECTION

Publications

ON SOME SYMMETRIES OF THE BASE n EXPANSION OF 1/m: THE CLASS NUMBER CONNECTION

Year : 2022

Publisher : Mathematical Sciences Publishers

Source Title : Pacific Journal of Mathematics

Document Type :

Abstract

Suppose that m≡1 mod 4 is a prime and that n≡3 mod 4 is a primitive root modulo m. We obtain a relation between the class number of the imaginary quadratic field Q(√−nm) and the digits of the base n expansion of 1/m. Secondly, if m ≡ 3 mod 4, we study some convoluted sums involving the base n digits of 1/m and arrive at certain congruence relations involving the class number of Q(√−m) modulo certain primes p which properly divide n+1.