THE EXPLICIT CONSTRUCTION OF RING CLASS FIELDS WITH APPLICATIONS TO QUADRATIC FORMS.
Item
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Title
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THE EXPLICIT CONSTRUCTION OF RING CLASS FIELDS WITH APPLICATIONS TO QUADRATIC FORMS.
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Identifier
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AAI8401952
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identifier
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8401952
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Creator
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PZENA, HOWARD SHELDON.
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Contributor
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Harvey Cohn
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Date
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1983
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics
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Abstract
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This thesis is in two parts. The first part is a summary of class field theory with emphasis on ring class fields. Cohn has devised a new method for computing ring class fields over an imaginary quadratic field. This technique is used here to compute the fields RCF {lcub}-64{rcub} an RCF {lcub}-128{rcub}. In the second part of the thesis the following two theorems are proved.;Theorem. Let m be a prime, m (TBOND) 1 mod p. Suppose that p is a prime and that p = X('2) +16mY('2) = U('2) + 32 m V('2). Then p = A('2) + 32B('2),;Theorem. If p (TBOND) 1 mod 8 and if q = 5, 13, or 37 then (q/p)4 = (-1)('b+d) where p = a('2) + 16b('2) = c('2) + 16qd('2) and ('(epsilon))q is the fundamental unit of the field (SQRT.(q)).;This last result resolves a conjecture of Emma Lehmer.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
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Program
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Mathematics
