mathematics, the genus is a classification of quadratic forms and lattices over the ring of integers. An integral quadratic form is a quadratic form on Zn, or...

In mathematics, a binary quadratic form is a quadratic homogeneous polynomial in two variables q ( x , y ) = a x 2 + b x y + c y 2 , {\displaystyle q(x...

Group (mathematics) Arithmetic genus Geometric genus Genus of a multiplicative sequence Genus of a quadratic form Spinor genus Popescu-Pampu 2016, p. xiii...

semigroup is the cardinality of the set of gaps in the numerical semigroup Genus of a quadratic form Grammatical gender Genus (music), a concept in ancient Greek...

mathematics, specifically the theory of quadratic forms, an ε-quadratic form is a generalization of quadratic forms to skew-symmetric settings and to *-rings;...

spinor genus is a classification of quadratic forms and lattices over the ring of integers, introduced by Martin Eichler. It refines the genus but may...

theory, a quadratic field is an algebraic number field of degree two over Q {\displaystyle \mathbf {Q} } , the rational numbers. Every such quadratic field...

significant extension of the theory of quadratic extensions, and the genus theory of quadratic forms (linked to the 2-torsion of the class group). As such...

signature theorem. Given a connected and oriented manifold M of dimension 4k, the cup product gives rise to a quadratic form Q on the 'middle' real cohomology...

number theory, a genus character of a quadratic number field K is a character of the genus group of K. In other words, it is a real character of the narrow...

real quadratic fields. In 2023 elliptic curves were proven to be modular over about half of imaginary quadratic fields, including fields formed by combining...

In mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by Turkish mathematician Cahit Arf (1941)...

Schottky form is the image of the Dedekind Delta function under the Ikeda lift. Igusa, Jun-ichi (1981), "Schottky's invariant and quadratic forms", E. B...

formula) is a formula for the sum of the weights of the lattices (quadratic forms) in a genus, weighted by the reciprocals of the orders of their automorphism...

i.e. the restriction of the intersection form to { H } ⊥ {\displaystyle \{H\}^{\perp }} is a negative definite quadratic form. This theorem is proven...

algebra of covariants is generated by the form itself of degree 1 and order 1. The algebra of invariants of the quadratic form F 2 ( x , y ) = A x 2 + 2...

variables. Siegel modular forms were first investigated by Carl Ludwig Siegel (1939) for the purpose of studying quadratic forms analytically. These primarily...

In algebraic geometry, a hyperelliptic curve is an algebraic curve of genus g > 1, given by an equation of the form y 2 + h ( x ) y = f ( x ) {\displaystyle...

⁠Θ(𝜏)/θ(𝜏)⁠ where θ(𝜏) is a modular form of weight ⁠1/2⁠ and Θ(𝜏) is a theta function of an indefinite binary quadratic form, and Dean Hickerson proved...

explicit quadratic and cubic generators of the ideal, showing that apart from the exceptions the cubics could be expressed in terms of the quadratics. In the...

algebraic groups and quadratic forms. It was introduced by J. Buhler and Z. Reichstein and in its most generality defined by A. Merkurjev. Basically...

members of a suitable finite field by connecting pairs of elements that differ by a quadratic residue. The Paley graphs form an infinite family of conference...

in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the existence of square roots...

elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined over a field K and...

terms of ideals and norms in quadratic fields. (A quadratic field consists of all numbers of the form a + b d {\displaystyle a+b{\sqrt {d}}} , where a {\displaystyle...

{\displaystyle w_{2}(M)} vanishes), then the signature of its intersection form, a quadratic form on the second cohomology group H 2 ( M ) {\displaystyle...

g)=g_{*}S(f)+S(g)} is thus the analogue of a 1-cocycle for the pseudogroup of biholomorphisms with coefficients in holomorphic quadratic differentials. Similarly φ...

accidentally hit a quadratic non-residue fairly quickly. If t is a quadratic residue, the p+1 method degenerates to a slower form of the p − 1 method...

value of the Arf invariant of a certain quadratic form Q with values mod 2. Thus in case of g = 3 and a plane quartic curve, there were 28 of one type...

1112/jlms/s1-41.1.193, MR 0199150 Cassels, J. W. S. (1978), Rational quadratic forms, London Mathematical Society Monographs, vol. 13, London-New York:...