Abstract
In this paper, we give an explicit lower bound for the class number of real quadratic field ℚd, where d=n2+4 is a square-free integer, using ωn which is the number of odd prime divisors of n.
Highlights
Let d be a positive square-free integer and let h(d) and Ck denote the class num√be r and the class group of a real quadratic field k Q( d ), respectively.e class number problem of quadratic fields is one of the most intriguing unsolved problems in Algebraic Number eory and has for a long time inspired the study of lower bounds of h(d).Many fruitful research studies have been conducted in this direction
E class number problem of quadratic fields is one of the most intriguing unsolved problems in Algebraic Number eory and has for a long time inspired the study of lower bounds of h(d)
We give a lower bound for h(n2 + 4), and √w e fi nd a necessary and sufficient condition for k Q( n2 + 4 ) to have class number ω(n) + 1
Summary
Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria Received 31 October 2019; Revised 21 December 2019; Accepted 8 January 2020; Published 30 January 2020 √ In this paper, we give an explicit lower bound for the class number of real quadratic field Q( d ), where d n2 + 4 is a square-free integer, using ω(n) which is the number of odd prime divisors of n.
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