Geodesic
An approximation formula for the shifted cubic moment of automorphic L-functions in the weight aspect
Canadian journal of mathematics, Tome 77 (2025) no. 3, pp. 715-738

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DOI

Consider the family of automorphic L-functions associated with primitive cusp forms of level one, ordered by weight k. Assuming that k tends to infinity, we prove a new approximation formula for the cubic moment of shifted L-values over this family which relates it to the fourth moment of the Riemann zeta function. More precisely, the formula includes a conjectural main term, the fourth moment of the Riemann zeta function and error terms of size smaller than that predicted by the recipe conjectures.
DOI : 10.4153/S0008414X23000512
Mots-clés : L-functions, cubic moment, weight aspect 
Balkanova, Olga; Conrey, John Brian; Frolenkov, Dmitry. An approximation formula for the shifted cubic moment of automorphic L-functions in the weight aspect. Canadian journal of mathematics, Tome 77 (2025) no. 3, pp. 715-738. doi: 10.4153/S0008414X23000512
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     title = {An approximation formula for the shifted cubic moment of automorphic {L-functions} in the weight aspect},
     journal = {Canadian journal of mathematics},
     pages = {715--738},
     year = {2025},
     volume = {77},
     number = {3},
     doi = {10.4153/S0008414X23000512},
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