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math.NT2024
Gerth's heuristics for a family of quadratic extensions of certain Galois number fields
C. G. K. Babu, R. Bera, J. Sivaraman +1
Gerth generalised Cohen-Lenstra heuristics to the prime . He conjectured that for any positive integer , the limit $$ \lim_{x \to \infty} \frac{\sum_{0 < D \le X, \atop{ \t…
math.NT2024
Linear Congruences and a Conjecture of Bibak
C. G. Karthick Babu, Ranjan Bera, B. Sury
We address three questions posed by Bibak \cite{KB20}, and generalize some results of Bibak, Lehmer and K G Ramanathan on solutions of linear congruences $\sum_{i=1}^k a_i x_i \equ…
math.NT2024
Linear Congruences in several variables with congruence restrictions
C. G. Karthick Babu, Ranjan Bera, B. Sury
In this article, we consider systems of linear congruences in several variables and obtain necessary and sufficient conditions as well as explicit expressions for the number of sol…