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searching for Modulus (algebraic number theory) 29 found (37 total)

alternate case: modulus (algebraic number theory)

Takagi existence theorem (827 words) [view diff] no match in snippet view article find links to article

formation Helmut Hasse, History of Class Field Theory, pp. 266–279 in Algebraic Number Theory, eds. J. W. S. Cassels and A. Fröhlich, Academic Press 1967. (See

Complex multiplication (1,926 words) [view diff] no match in snippet view article find links to article

particular points. It has also turned out to be a central theme in algebraic number theory, allowing some features of the theory of cyclotomic fields to be

Class number formula (1,256 words) [view diff] no match in snippet view article find links to article

be replaced by Dirichlet characters (via class field theory) for some modulus f called the conductor. Therefore all the L(1) values occur for Dirichlet

Power residue symbol (1,233 words) [view diff] no match in snippet view article find links to article

In algebraic number theory the n-th power residue symbol (for an integer n > 2) is a generalization of the (quadratic) Legendre symbol to n-th powers

Cubic reciprocity (3,831 words) [view diff] no match in snippet view article find links to article

Cubic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x3 ≡ p (mod q)

Gauss sum (899 words) [view diff] no match in snippet view article find links to article

In algebraic number theory, a Gauss sum or Gaussian sum is a particular kind of finite sum of roots of unity, typically G(χ):=G(χ,ψ)=∑χ(r)⋅ψ(r){\displaystyle

Quartic reciprocity (4,600 words) [view diff] no match in snippet view article find links to article

biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x4 ≡ p (mod q)

Gaussian integer (4,706 words) [view diff] no match in snippet view article find links to article

to 3 modulo 4, then it is a Gaussian prime; in the language of algebraic number theory, p is said to be inert in the Gaussian integers. If p is congruent

Integer factorization (2,968 words) [view diff] no match in snippet view article find links to article

been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing. Not all numbers of a given length are equally

Dirichlet's theorem on arithmetic progressions (2,843 words) [view diff] no match in snippet view article find links to article

generalizes to more than one polynomial with degree larger than one. In algebraic number theory, Dirichlet's theorem generalizes to Chebotarev's density theorem

Legendre symbol (2,221 words) [view diff] no match in snippet view article find links to article

symbol inspired introduction of several other "symbols" used in algebraic number theory, such as the Hilbert symbol and the Artin symbol. Let p{\displaystyle

Prime number (13,980 words) [view diff] no match in snippet view article find links to article

search for an explanation for this phenomenon led to the deep algebraic number theory of Heegner numbers and the class number problem. The Hardy–Littlewood

Baby-step giant-step (1,028 words) [view diff] no match in snippet view article find links to article

inversion as proposed in. H. Cohen, A course in computational algebraic number theory, Springer, 1996. D. Shanks, Class number, a theory of factorization

Complex number (11,261 words) [view diff] no match in snippet view article find links to article

called algebraic numbers – they are a principal object of study in algebraic number theory. Compared to Q¯{\displaystyle {\overline {\mathbb {Q} }}}, the

List of theorems (5,993 words) [view diff] no match in snippet view article find links to article

algebra) Binomial theorem (algebra, combinatorics) Birch's theorem (algebraic number theory) Birkhoff–Grothendieck theorem (complex geometry) Birkhoff–Von

Eisenstein's criterion (3,476 words) [view diff] no match in snippet view article find links to article

reduction mod p. It does however allow one to see, in terms of algebraic number theory, how frequently Eisenstein's criterion might apply, after some

Quadratic reciprocity (8,009 words) [view diff] no match in snippet view article find links to article

Every textbook on elementary number theory (and quite a few on algebraic number theory) has a proof of quadratic reciprocity. Two are especially noteworthy:

Riemann zeta function (9,698 words) [view diff] no match in snippet view article find links to article

ISBN 0-12-232750-0. Zbl 0315.10035. Neukirch, Jürgen (1999). Algebraic number theory. Springer. p. 422. ISBN 3-540-65399-6. Hashimoto, Yasufumi; Iijima

Safe and Sophie Germain primes (2,617 words) [view diff] no match in snippet view article find links to article

Harold M. (2000), Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory, Graduate Texts in Mathematics, vol. 50, Springer, pp. 61–65, ISBN 9780387950020

Jacobi symbol (2,207 words) [view diff] no match in snippet view article find links to article

See Cohen, p. 495 Cohen, Henri (1993). A Course in Computational Algebraic Number Theory. Berlin: Springer. ISBN 3-540-55640-0. Ireland, Kenneth; Rosen

Arithmetic (16,349 words) [view diff] no match in snippet view article find links to article

theory include elementary number theory, analytic number theory, algebraic number theory, and geometric number theory. Elementary number theory studies

Latin letters used in mathematics, science, and engineering (3,829 words) [view diff] no match in snippet view article find links to article

Hamiltonian in Hamiltonian mechanics. h represents: the class number in algebraic number theory a small increment in the argument of a function the unit hour for

Hensel's lemma (8,293 words) [view diff] no match in snippet view article find links to article

maint: location missing publisher (link) Neukirch, Jürgen (1999). Algebraic Number Theory. Berlin, Heidelberg: Springer Berlin Heidelberg. ISBN 978-3-662-03983-0

Lemniscate elliptic functions (19,411 words) [view diff] no match in snippet view article find links to article

{1}{2}}\operatorname {aclh} (c){\bigr ]}^{2}\end{aligned}}} In algebraic number theory, every finite abelian extension of the Gaussian rationals Q(i){\displaystyle

Ideal lattice (5,571 words) [view diff] no match in snippet view article find links to article

‘algebraic’ and ‘geometric’ components of the reduction. They used algebraic number theory, in particular, the canonical embedding of a number field and the

Euclidean algorithm (14,766 words) [view diff] no match in snippet view article find links to article

Edwards, H. (2000). Fermat's last theorem: a genetic introduction to algebraic number theory. Springer. p. 76. Cohn 1962, pp. 104–110 LeVeque, W. J. (2002)

Pi (16,888 words) [view diff] no match in snippet view article find links to article

Hecke's zeta-functions". In Cassels, J. W. S.; Fröhlich, A. (eds.). Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965). Thompson, Washington

Proof of Fermat's Last Theorem for specific exponents (5,149 words) [view diff] no match in snippet view article find links to article

(2008-05-23). Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory. Graduate Texts in Mathematics. Vol. 50 (3rd printing 2000 ed.)

Group (mathematics) (12,886 words) [view diff] no match in snippet view article

ISBN 978-0-486-43235-9, MR 2044239. Neukirch, Jürgen (1999), Algebraic Number Theory, Grundlehren der mathematischen Wissenschaften, vol. 322, Berlin: