Diophantine inequalities

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Starting with the work of I.M. Vinogradov and H. Heilbronn, the author develops the theme of nonlinear Diophantine approximation in a number of different directions.

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Title Statements

Full title :Diophantine inequalities / R.C. Baker.

Summary

Starting with the work of I.M. Vinogradov and H. Heilbronn, the author develops the theme of nonlinear Diophantine approximation in a number of different directions.

Edition Statements

Publication Date:1986.

Publication Statements

Publisher(s):Clarendon Press, Oxford University Press
Place of Publication:Oxford [Oxfordshire]
Language:eng
Publication Date:1986.

The Physical Object

Description:xii, 275 pages : : illustrations ; : 24 cm

Edition Identifiers

ISBN:0198535457, 9780198535454
oclc:ocm13007299
LC Classification:QA242
Dewey Decimal:512/.73

Introduction -- Fourier analysis -- Heilbronn's theorem and Schmidt's extension -- Vinogradov's mean value method -- The solution of Davenport's problem -- The method of sums of kth powers -- Schmidt's lattice method -- The lattice method for polynomials of arbitrary degree -- Quadratic forms -- Simultaneous approximation for quadratic forms and additive forms -- Nonnegative solutions of additive equations -- Small solutions of additive congruences -- Small solutions of additive equations of odd degree -- Diophantine inequalities for forms of odd degree -- Exponential sums: forms with integer coefficients -- The invariants g and h -- Exponential sums: polynomials on a finite group -- Small solutions of congruences to general modulus.