Algebraic Numbers and Algebraic Functions by Cohn P.M.

By Cohn P.M.

Show description

Read Online or Download Algebraic Numbers and Algebraic Functions PDF

Similar abstract books

A Primer on Mapping Class Groups (Princeton Mathematical)

The learn of the mapping type crew Mod(S) is a classical subject that's experiencing a renaissance. It lies on the juncture of geometry, topology, and team concept. This e-book explains as many very important theorems, examples, and strategies as attainable, speedy and at once, whereas while giving complete info and maintaining the textual content approximately self-contained.

Functional analysis and differential equations in abstract spaces, 1st Edition

Sensible research and Differential Equations in summary areas offers an simple therapy of this very classical topic-but provided in a slightly targeted manner. the writer bargains the useful research interconnected with really good sections on differential equations, therefore making a self-contained textual content that incorporates lots of the valuable sensible research historical past, frequently with relatively whole proofs.

Extra info for Algebraic Numbers and Algebraic Functions

Sample text

Faltings and G. , Vieweg, 1992). Zimmer, Computing the Mordell-Weil Group of an Elliptic Curve over Q, in Elliptic Curves and Related Topics (ed. Kisilevsky and M. Ram Murthy), CRM Proceedings and Lecture Notes, vol 4, pp 61-83 (Amer. Math. , 1994). Gross, Kolyvagin’s work on modular elliptic curves, in L-functions and Arithmetic ed. Taylor (Cambridge, 1991). Zagier, Heegner points and derivatives of L-series II, Math. Ann. 278(1987), 497-562. Zagier, Heegner points and derivatives of L-series, Invent.

For suppose that u0 , v0 have been so chosen that there is only one good prime p0 which divides c(u0 , v0 ); then the product in (7) reduces to the left hand side of (6), and so (6) holds for this prime. Now choose an open set N ⊂ S0 such that (7) holds throughout N for each c(u, v); by a slightly modified version of Schinzel’s Hypothesis we can choose (u0 , v0 ) in N so that every c(u0 , v0 ) is the product of one good prime and possibly some factors in B. As c runs through all irreducible factors of a1 a2 a3 , p0 runs through all those primes for 21 which we have to verify (6).

David, (Cambridge, 1996). Heath-Brown, The Density of Rational Points on Cayley’s Cubic Surface, (unpublished). Hooley, On nonary cubic forms, J. Reine Angew. , 386(1988), 32-98 and 415(1991), 95-165 and 456(1994), 53-63. Hulsbergen, Conjectures in Arithmetic Algebraic Geometry, (Vieweg, 1992). Kleiman, Algebraic cycles and the Weil conjectures, in Dix expos´es sur la cohomologie des sch´emas, ed. Kuiper (NorthHolland, 1968). Kolyvagin, Finiteness of E(Q) and X(E/Q) for a class of Weil curves, Izv.

Download PDF sample

Rated 4.39 of 5 – based on 33 votes