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141
SpaceTime Diversity Systems Based on Linear Constellation Precoding
 IEEE TRANS. WIRELESS COMMUN
, 2003
"... We present a unified approach to designing spacetime (ST) block codes using linear constellation precoding (LCP). Our designs are based either on parameterizations of unitary matrices, or on algebraic numbertheoretic constructions. With an arbitrary number of transmit and receiveantennas, STLCP ..."
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Cited by 87 (8 self)
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We present a unified approach to designing spacetime (ST) block codes using linear constellation precoding (LCP). Our designs are based either on parameterizations of unitary matrices, or on algebraic numbertheoretic constructions. With an arbitrary number of transmit and receiveantennas, STLCP achieves rate 1 symbol/s/Hz and enjoys diversity gain as high as over (possibly correlated) quasistatic and fast fading channels. As figures of merit, we use diversity and coding gains, as well as mutual information of the underlying multipleinputmultipleoutput system. We show that over quadratureamplitude modulation and pulseamplitude modulation, our LCP achieves the upper bound on the coding gain of all linear precoders for certain values of and comes close to this upper bound for other values of , in both correlated and independent fading channels. Compared with existing ST block codes adhering to an orthogonal design (STOD), STLCP offers not only better performance, but also higher mutual information for...
GENERAL CONGRUENCES FOR BERNOULLI POLYNOMIALS
 DISCRETE MATH. 262(2003), 253–276.
, 2003
"... In this paper we establish some explicit congruences for Bernoulli polynomials modulo a general positive integer. In particular Voronoi’s and Kummer’s congruences are vastly extended. ..."
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Cited by 35 (32 self)
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In this paper we establish some explicit congruences for Bernoulli polynomials modulo a general positive integer. In particular Voronoi’s and Kummer’s congruences are vastly extended.
Congruences concerning Bernoulli numbers and Bernoulli polynomials
 Discrete Appl. Math
, 2000
"... Let {Bn(x)} denote Bernoulli polynomials. In this paper we generalize Kummer’s congruences by determining Bk(p−1)+b(x)=(k(p − 1) + b) (mod p n), where p is an odd prime, x is a pintegral rational number and p − 1 b. As applications we obtain explicit formulae for ∑p−1 x=1 (1=xk) (mod p 3); ∑ (p−1 ..."
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Cited by 24 (16 self)
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Let {Bn(x)} denote Bernoulli polynomials. In this paper we generalize Kummer’s congruences by determining Bk(p−1)+b(x)=(k(p − 1) + b) (mod p n), where p is an odd prime, x is a pintegral rational number and p − 1 b. As applications we obtain explicit formulae for ∑p−1 x=1 (1=xk) (mod p 3); ∑ (p−1)=2 (1=x
Examples of genus two CM curves defined over the rationals
 Math. Comp
, 1999
"... Abstract. We present the results of a systematic numerical search for genus two curves defined over the rationals such that their Jacobians are simple and have endomorphism ring equal to the ring of integers of a quartic CM field. Including the wellknown example y 2 = x 5 − 1 we find 19 nonisomorp ..."
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Cited by 20 (1 self)
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Abstract. We present the results of a systematic numerical search for genus two curves defined over the rationals such that their Jacobians are simple and have endomorphism ring equal to the ring of integers of a quartic CM field. Including the wellknown example y 2 = x 5 − 1 we find 19 nonisomorphic such curves. We believe that these are the only such curves. 1.
Planar coincidences for Nfold symmetry
, 2005
"... The coincidence problem for planar patterns with Nfold symmetry is considered. For the Nfold symmetric module with N < 46, all isometries of the plane are classified that result in coincidences of finite index. This is done by reformulating the problem in terms of algebraic number fields and using ..."
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Cited by 16 (11 self)
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The coincidence problem for planar patterns with Nfold symmetry is considered. For the Nfold symmetric module with N < 46, all isometries of the plane are classified that result in coincidences of finite index. This is done by reformulating the problem in terms of algebraic number fields and using prime factorization. The more complicated case N ≥ 46 is briefly discussed and N = 46 is described explicitly. The results of the coincidence problem also solve the problem of colour lattices in two dimensions and its natural generalization to colour modules.
Topological properties of Eschenburg spaces and 3Sasakian manifolds
 MATHEMATISCHE ANNALEN
, 2005
"... We examine topological properties of the sevendimensional positively curved Eschenburg biquotients and find many examples which are homeomorphic but not diffeomorphic. A special subfamily of these manifolds also carries a 3Sasakian metric. Among these we construct a pair of 3Sasakian spaces which ..."
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Cited by 15 (9 self)
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We examine topological properties of the sevendimensional positively curved Eschenburg biquotients and find many examples which are homeomorphic but not diffeomorphic. A special subfamily of these manifolds also carries a 3Sasakian metric. Among these we construct a pair of 3Sasakian spaces which are diffeomorphic to each other, thus giving rise to the first example of a manifold which carries two nonisometric 3Sasakian metrics.
BlochKato conjecture and Main Conjecture of Iwasawa theory for Dirichlet characters
, 2002
"... The Tamagawa number conjecture proposed by S. Bloch and K. Kato describes the “special values ” of Lfunctions in terms of cohomological data. The main conjecture of Iwasawa theory describes a padic Lfunction in terms of the structure of modules for the Iwasawa algebra. We give a complete proof of ..."
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Cited by 14 (2 self)
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The Tamagawa number conjecture proposed by S. Bloch and K. Kato describes the “special values ” of Lfunctions in terms of cohomological data. The main conjecture of Iwasawa theory describes a padic Lfunction in terms of the structure of modules for the Iwasawa algebra. We give a complete proof of both conjectures (up to the prime 2) for Lfunctions attached to Dirichlet characters. We use the insight of Kato and B. PerrinRiou that these two conjectures can be seen as incarnations of the same mathematical content. In particular, they imply each other. By a bootstrapping process using the theory of Euler systems and explicit reciprocity laws, both conjectures are reduced to the analytic class number formula. Technical problems with primes dividing the order of the character are avoided by using the correct cohomological formulation of the main conjecture.
Quantum cyclotomic orders of 3manifolds
 Topology
"... Abstract. This paper provides a topological interpretation for number theoretic properties of quantum invariants of 3manifolds. In particular, it is shown that the padic valuation of the quantum SO(3)invariant of a 3manifold M, for odd primes p, is bounded below by a linear function of the mod p ..."
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Cited by 13 (1 self)
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Abstract. This paper provides a topological interpretation for number theoretic properties of quantum invariants of 3manifolds. In particular, it is shown that the padic valuation of the quantum SO(3)invariant of a 3manifold M, for odd primes p, is bounded below by a linear function of the mod p first betti number of M. Sharper bounds using more delicate topological invariants are given as well. Since the birth of quantum topology in the last decade [Jo][Wi], one of the fundamental problems facing topologists has been to find topological interpretations for the vast array of quantum invariants that have come to light. One common characteristic among these invariants is their rich number theoretic content, and it has been a