Extension of a theorem of Cauchy and Jacobi

DOI10.1016/0022-314X(84)90075-1zbMath0551.12014MaRDI QIDQ801117

Richard H. Hudson, Duncan A. Buell, Kenneth S. Williams

Publication date: 1984

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

exponential sumsfinite fieldsclass numberquadratic fieldquaternary quadratic formscongruences for binomial coefficientscyclotomic problemimaginary quartic fieldproducts of factorialsquartic residuesrepresentation of prime powers by binary quadratic forms

Mathematics Subject Classification ID

General ternary and quaternary quadratic forms; forms of more than two variables (11E20) Arithmetic theory of polynomial rings over finite fields (11T55) Cyclotomy (11T22) Power residues, reciprocity (11A15)

Cites Work

• Gauss sums and elliptic functions. II: The quartic sum
• Sums of Gauss, Jacobi, and Jacobsthal
• On Euler's criterion
• Binomial Coefficients and Jacobi Sums
• The Determination of all Imaginary, Quartic, Abelian Number Fields With Class Number 1
• The determination of Gauss sums
• An application of a formula of Western to the evaluation of certain Jacobsthal sums
• On the Uniqueness of Solutions of Certain Diophantine Equations
• Some conjectures concerning Gauss sums.
• Cyclotomy and Trinomial Congruences
• On a conjecture of hasse concerning multiplicative relations of Gaussian sums

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