## Transactions of the American Mathematical Society, Volume 22 |

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Abelian varieties algebraic algebraic curves algebraic cycles algebraic surface arbitrary assume birational transformation chain changes sign characteristic equation circle completely reduced polynomials complex multiplication condition consider constant contains corresponding cycles defined degree denote derivatives determined differential equations divisors elements equal equivalent exists expressed factor follows formal covariants fundamental genus geodesic given Hence Hermitian form hypersurfaces identical independent integers integral coefficients intersection interval irreducible leading terms Lemma linear system m/di Mathematical matrix modular invariants modulo normal segments notation obtained pairs paper paraphrases period matrix periods permutable plane polynomial polynomial with integral positive integer proof proved quadratic rational reduced curve relation replaced residual congruences residue system modulo respectively Riemann Riemann form roots satisfied second kind seminvariants Seminvariants led seminvariants whose leading solution subset surface tangent Theorem tions values vanish variables zero divisors

### Popular passages

Page 101 - On the location of the roots of the Jacobian of two binary forms, and of the derivative of a rational function,

Page 160 - Sur l'ordre de la meilleure approximation des fonctions continues par des polynômes de degré donné, Mémoires de l'Académie Royale de Belgique (2) 4 (1912), 1 — 104.

Page 80 - Die geometrischen Constructionen, ausgeführt mittelst der geraden Linie und eines festen Kreises, als Lehrgegenstand auf höheren Unterrichtsanstalten und zur praktischen Benutzung.

Page 101 - The vanishing of the jacobian of two binary forms f\ and /2 of degrees p\ and p» respectively determines the points of equilibrium in the field of force due to...

Page 266 - Existence Theorems for the General Real Self-Adjoint Linear System of the Second Order." II. "Oscillation Theorems for the Real Self-Adjoint Linear System of the Second Order.

Page 101 - ... 19 (1918), p. 43). The identity of the logarithmic derivative is used, but the mechanical analogy and Jensen's theorem are not cited. So far we have been concerned only with theorems of relative distribution for the roots of a polynomial and of its derivative. In a most suggestive paper by Bocher ("A Problem in Statics and its Relation to Certain Algebraic Invariants," Proceedings of the American Academy of Arts and Sciences, Vol.

Page 51 - ABC is the set of all points \X] such that X lies on a segment whose end points are on different sides of the triangle ABC.

Page 103 - Our next remark is stated explicitly as a lemma. It is readily stated and established for regions whose boundaries are curves much more general than circles, but we consider here merely the form under the hypothesis of Theorem II and for application to the proof of that theorem. advantages over the following suggested method of proof. The theorem is evidently true when Ci , Ct , and €3 are points. The theorem is easily proved when C\ and C^ are points but C

Page 219 - Legendre symbol; and e(n) equals 1 or 0 according as n is or is not the square of an integer.

Page 45 - There exists a simple chain of .S'i -elements, of rank 2, from E to F. This process may be continued. It follows that there exists a sequence of...