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We propose a recipe for constructing a SIC fiducial vector in complex Hilbert space of dimension of the form $d=n^2+3$, focussing on prime dimensions $d=p$.
Mathematical problems
D. Hilbert · 1902
Earlier work this paper cites.
Méthode pour la détermination de valeurs statistiques d’observations concernant des grandeurs soumises à des fluctuations irrégulières
A. Einstein · 1914
Earlier work this paper cites.
Some problems of ‘ partitio numerorum
G. H. Hardy and J. E. Littlewood · 1923
Earlier work this paper cites.
Theory of Groups and Quantum Mechanics
H. Weyl · 1932
Earlier work this paper cites.
Introduction to Cyclotomic Fields
L. C. Washington · 1934
Earlier work this paper cites.
Congruence properties of Tchebycheff polynomials
T. Bang · 1954
Earlier work this paper cites.
On the conjecture of Hardy & Littlewood concerning the number of primes of the form n 2 + a n^{2}+a
D. Shanks · 1960
Earlier work this paper cites.
Algebraic Number Theory
J. W. S. Cassels and A. Fröhlich, editors · 1967
Earlier work this paper cites.
On real quadratic fields containing units with norm − 1 -1
H. Yokoi · 1968
Earlier work this paper cites.
Introduction to Commutative Algebra
M. F. Atiyah and I. G. MacDonald · 1969
Earlier work this paper cites.
Fast evaluation and interpolation
H. T. Kung · 1973
Earlier work this paper cites.
L L -functions at s = 1 s=1 . III. Totally real fields and Hilbert’s twelfth problem
H. M. Stark · 1976
Earlier work this paper cites.
A Classical Invitation to Algebraic Numbers and Class Fields
H. Cohn · 1978
Earlier work this paper cites.
Local Fields
J.-P. Serre · 1979
Earlier work this paper cites.
L L -functions at s = 1 s=1 . IV. First derivatives at s = 0 s=0
H. M. Stark · 1980
Earlier work this paper cites.
Advanced Number Theory
H. Cohn · 1980
Earlier work this paper cites.
On Stark’s conjectures on the behaviour of L ( s , χ ) L(s,\chi) at s = 0 s=0
J. C. Tate · 1982
Earlier work this paper cites.
Les Conjectures de Stark sur les Fonctions L L d’Artin en s = 0 s=0
J. C. Tate · 1984
Earlier work this paper cites.
On the Stark-Shintani conjecture and certain relative class numbers
T. Arakawa · 1985
Earlier work this paper cites.
Algebraic Number Theory
S. Lang · 1986
Earlier work this paper cites.
Local Fields
J. W. S. Cassels · 1986
Earlier work this paper cites.
Class Field Theory
J. Neukirch · 1986
Earlier work this paper cites.
Tata Lectures on Theta III
D. Mumford with M. Nori and P. Norman · 1991
Cited alongside, same era.
The Magma Algebra System I: The User Language
W. Bosma, J. J. Cannon, and C. Playoust · 1996
Cited alongside, same era.
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G. Zauner · 1999
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X.-F. Roblot · 2000
Cited alongside, same era.
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