Abstract
AbstractLet K be a real quadratic number field and let p be a prime number which is inert in K. We denote the completion of K at the place p by Kp. We propose a p-adic construction of special elements in Kp× and formulate the conjecture that they should be p-units lying in narrow ray class fields of K. The truth of this conjecture would entail an explicit class field theory for real quadratic number fields. This construction can be viewed as a natural generalization of a construction obtained by Darmon and Dasgupta who proposed a p-adic construction of p-units lying in narrow ring class fields of K.
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