The universality of zeta-functions attached to certain cusp forms (Q2717634)
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scientific article; zbMATH DE number 1605229
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The universality of zeta-functions attached to certain cusp forms |
scientific article; zbMATH DE number 1605229 |
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The universality of zeta-functions attached to certain cusp forms (English)
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17 June 2001
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universality
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cusp forms
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zeta-functions
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An analogue of Voronin's universality theorem for cusp form zeta-functions was proved by \textit{A. Kačenas} and \textit{A. Laurinčikas} [Liet. Mat. Rink. 38, 82-97 (1998; Zbl 0929.11064)], but only under the assumption of a certain hypothesis on the Fourier coefficients \(c_p\), for primes \(p\), of the cusp form in question. In the present paper, an unconditional proof is given; the main new ingredient is an asymptotic formula for the sum function of \(c_p^2\).
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