Greenberg's conjecture for real quadratic number fields

Key Points

• The orders of the 3-class groups remain bounded as n increases, consistent with Greenberg's conjecture.
• This research computes the 3-class groups for real quadratic fields with discriminants less than 100,000.
• The analysis focuses on the cyclotomic extensions of the real quadratic fields.
• Findings support the conjecture's validity, providing insights into the structure of these number fields.