Abstract
Additive twists are important invariants associated to holomorphic cusp forms; they encode the Eichler–Shimura isomorphism and contain information about automorphic L-functions. In this paper we prove that central values of additive twists of the L-function associated to a holomorphic cusp form f of even weight k are asymptotically normally distributed. This generalizes (to
Acknowledgements
I would like to express my gratitude to my advisor Morten Risager for suggesting this problem to me and for our countless stimulating discussions. I would also like to thank Yiannis Petridis for his time and insight.
References
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Articles in the same Issue
- Frontmatter
- Local existence and uniqueness of skew mean curvature flow
- Characteristic cycle and wild ramification for nearby cycles of étale sheaves
- Theta correspondence for p-adic dual pairs of type I
- Residues on affine Grassmannians
- The tight approximation property
- Free boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial disc
- Central values of additive twists of cuspidal L-functions
- On the geometric André–Oort conjecture for variations of Hodge structures
Articles in the same Issue
- Frontmatter
- Local existence and uniqueness of skew mean curvature flow
- Characteristic cycle and wild ramification for nearby cycles of étale sheaves
- Theta correspondence for p-adic dual pairs of type I
- Residues on affine Grassmannians
- The tight approximation property
- Free boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial disc
- Central values of additive twists of cuspidal L-functions
- On the geometric André–Oort conjecture for variations of Hodge structures