International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 7, Pages 387-406
New versions of the
Nyman-Beurling criterion for the Riemann hypothesis
Departamento de Matemáticas, Instituto Venezolano de Investigaciones Científicas, Apartado 21827, Caracas 1020-A, Venezuela
Received 15 May 2001; Revised 19 February 2002
Copyright © 2002 Luis Báez-Duarte. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let , , , and , where is the Möbius function. Norms are in , . For it is noted that in is equivalent to for all . The space is the linear space generated by the functions with . Define . For all we prove the following theorems: (I) implies , and implies for all . (II) implies in , and in implies for all .