Prime producing quadratic polynomials and class-number one problem for real quadratic fields
نویسندگان
چکیده
منابع مشابه
New Prime-Producing Quadratic Polynomials Associated with Class Number One or Two
This article provides necessary and sufficient conditions for a real quadratic field to have class number one or two in terms of a new set of primeproducing quadratic polynomials
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a4 + 1 a5 + .. . will see that a less wasteful notation, say [ a0 , a1 , a2 , . . . ] , is needed to represent it. Anyone attempting to compute the truncations [ a0 , a1 , . . . , ah ] = ph/qh will be delighted to notice that the definition [ a0 , a1 , . . . , ah ] = a0 + 1/[ a1 , . . . , ah ] immediately implies by induction on h that there is a correspondence ( a0 1 1 0 ) ( a1 1 1 0 ) · · · (...
متن کاملQuadratic polynomials producing consecutive, distinct primes and class groups of complex quadratic fields
1. Introduction. For centuries there has been a fascination with prime-producing quadratic polynomials. We will describe the relationship between such polynomials and class groups of complex quadratic fields with exponent 1 or 2. In Section 2, we set up the notation and preliminaries including a consequence of a result which we proved in [15], namely Theorem 2.3. We illustrate how all the conse...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1990
ISSN: 0386-2194
DOI: 10.3792/pjaa.66.119