This article is cited in 21 papers

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

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


Abstract: 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.

UDC: 511

MSC: 11F66, 11M41, 11K99

Received: 28.02.2002

DOI: 10.4213/im419

 English version: Izvestiya: Mathematics, 2003, 67:1, 77–90

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