A converse to linear independence criteria, valid almost everywhere

TY - JOUR

T1 - A converse to linear independence criteria, valid almost everywhere

AU - Fischler, S.

AU - Hussain, M.

AU - Kristensen, Simon

AU - Levesley, J.

PY - 2015

Y1 - 2015

N2 - We prove a weighted analogue of the Khintchine-Groshev theorem, where the distance to the nearest integer is replaced by the absolute value. This is applied to proving the optimality of several linear independence criteria over the field of rational numbers.

AB - We prove a weighted analogue of the Khintchine-Groshev theorem, where the distance to the nearest integer is replaced by the absolute value. This is applied to proving the optimality of several linear independence criteria over the field of rational numbers.

KW - METRIC THEORY

KW - ZETA-FUNCTION

KW - ODD INTEGERS

KW - APPROXIMATIONS

KW - IRRATIONALITY

KW - VALUES

KW - FORMS

U2 - 10.1007/s11139-014-9662-8

DO - 10.1007/s11139-014-9662-8

M3 - Journal article

SN - 1382-4090

VL - 38

SP - 513

EP - 528

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 3

ER -