zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A family of Hadamard matrices of dihedral group type. (English) Zbl 0943.05026
Summary: Let D 2n be a dihedral group of order 2n and be the rational integer ring where n is an odd integer. Kimura gave the necessary and sufficient conditions such that a matrix of order 8n+4 obtained from the elements of the group ring [D 2n ] becomes a Hadmard matrix. We show that if p1(mod4) is an odd prime and q=2p-1 is a prime power, then there exists a family of Hadamard matrices of dihedral group type. We prove this theorem by giving the elements of [D 2p ] concretely. The Gauss sum over GF(p) and the relative Gauss sum over GF(q 2 ) are important to prove the theorem.
05B20Matrices (incidence, Hadamard, etc.)
11L05Gauss and Kloosterman sums