Xuejun Guo, Hourong Qin
Abstract
In this article, we prove that an imaginary quadratic field F has the ideal class group isomorphic to ℤ/2ℤ ⊕ ℤ/2ℤ if and only if the Ono number of F is 3 and F has exactly 3 ramified primes under the Extended Riemann Hypothesis (ERH). In addition, we give the list of all imaginary quadratic fields with Ono number 3.
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In this article, we prove that an imaginary quadratic field F has the ideal class group isomorphic to ℤ/2ℤ ⊕ ℤ/2ℤ if and only if the Ono number of F is 3 and F has exactly 3 ramified primes under the Extended Riemann Hypothesis (ERH). In addition, we give the list of all imaginary quadratic fields with Ono number 3.
Key concepts: Mathematics, The Imaginary, Quadratic equation, Quadratic field, Ideal (ethics), Class number, Ideal class group, Riemann hypothesis