Abstract
An automorphic self dual L-function has the super-positivity property if all derivatives of the completed L-function at the central point \(s=1/2\) are nonnegative and all derivatives at a real point \(s > 1/2\) are positive. In this paper, we prove that at least 12% of L-functions associated to Hecke basis cusp forms of weight 2 and large prime level q have the super-positivity property. It is also shown that at least 49% of such L-functions have no real zeros on \( \mathrm{Re}(s) > 0\) except possibly at \(s = 1/2.\)
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Goldfeld, D., Huang, B. Super-positivity of a family of L-functions in the level aspect. Res Math Sci 5, 16 (2018). https://doi.org/10.1007/s40687-018-0134-4
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DOI: https://doi.org/10.1007/s40687-018-0134-4