... Title 111 Series QA247.S23 1983 512' 74 8 2-2 0053 ISBN 0-5 3 4-9 8049-X Algebraic Numbers and Fourier Analysis RAPHAEL SALEM T o the memory of my father - to the memory o my nephew, Emmanuel Amar, ... distinct real zeros between -2 and +2 The equation + has then m - I real roots (algebraic integers) between -2 and +2, and one real m root between r and r em(em> 0, e -+ as m ,co) Putting + we ... impossible since T > and a: = ( Hence, we have proved the linear independence of the wj and Now, we have, modulo 1, "1 7" + - + (8-i-i + e-tfi-I) 7'" t This argument is due to Pisot C j-1 - (mod I) Pb,...