Multiplicity one for $L$-functions and applications
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2013
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| _version_ | 1866918015922077696 |
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| author | Farmer, David W. Pitale, Ameya Ryan, Nathan C. Schmidt, Ralf |
| author_facet | Farmer, David W. Pitale, Ameya Ryan, Nathan C. Schmidt, Ralf |
| contents | We give conditions for when two Euler products are the same given that they satisfy a functional equation and their coefficients are not too large and do not differ from each other by too much. Additionally, we prove a number of multiplicity one type results for the number-theoretic objects attached to $L$-functions. These results follow from our main result, which has slightly weaker hypotheses than previous multiplicity one theorems for $L$-functions. Significantly stronger results are available when the L-function is known to be automorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1305_3972 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Multiplicity one for $L$-functions and applications Farmer, David W. Pitale, Ameya Ryan, Nathan C. Schmidt, Ralf Number Theory We give conditions for when two Euler products are the same given that they satisfy a functional equation and their coefficients are not too large and do not differ from each other by too much. Additionally, we prove a number of multiplicity one type results for the number-theoretic objects attached to $L$-functions. These results follow from our main result, which has slightly weaker hypotheses than previous multiplicity one theorems for $L$-functions. Significantly stronger results are available when the L-function is known to be automorphic. |
| title | Multiplicity one for $L$-functions and applications |
| topic | Number Theory |
| url | https://arxiv.org/abs/1305.3972 |