The universality of $L$-functions associated with new forms

A. P. Laurincikas ; K. Matsumoto ; J. Steuding

Izvestiya. Mathematics , Tome 67 (2003) no. 1, pp. 77-90.

Résumé

We prove the universality theorem for $L$-functions of new parabolic forms. It concerns the uniform approximation of analytic functions by shifts of these $L$-functions. This theorem together with the Shimura–Taniyama conjecture (now proved) yields the universality of $L$-functions of non-singular elliptic curves over the field of rational numbers. The universality of $L$-functions implies that they are functionally independent.

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