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• W2074273396 abstract "We consider a system of M independent, inhomogeneous linear equations in N > M variables having coefficients in an algebraic number field k. We give a best possible lower bound on the inhomogeneous height of a solution vector in k N and determine when a solution exists in (O s ) N , where O s is the ring of S-integers in k. If such a system has a solution vector in (O s ) N , we show that it has a solution ζ in (O s ) N such that the inhomogeneous height of ζ is relatively small. We give an explicit upper bound for this height in terms of the heights of the matrices defining the linear system. Our method uses geometry of numbers over adele spaces and local to global arguments" @default.
• W2074273396 created "2016-06-24" @default.
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• W2074273396 date "1993-02-01" @default.
• W2074273396 modified "2023-09-24" @default.
• W2074273396 title "Small solutions to inhomogeneous linear equations over number fields" @default.
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• W2074273396 doi "https://doi.org/10.1090/s0002-9947-1993-1094559-2" @default.
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