An elliptic curve test of the L-Functions Ratios Conjecture
We compare the L-Function Ratios Conjecture's prediction with number theory for the family of quadratic twists of a fixed elliptic curve with prime conductor, and show agreement in the 1-level density up to an error term of size X^{-(1-sigma)/2} for test functions supported in (-sigma, sigma);...
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | We compare the L-Function Ratios Conjecture's prediction with number theory
for the family of quadratic twists of a fixed elliptic curve with prime
conductor, and show agreement in the 1-level density up to an error term of
size X^{-(1-sigma)/2} for test functions supported in (-sigma, sigma); this
gives us a power-savings for \sigma |
|---|---|
| DOI: | 10.48550/arxiv.1011.3298 |