2018/07/26 by Samuele Anni, Gebhard Boeckle, Anni, Samuele +5
Mathematics · #11F33 #11F85 Secondary: 11F67 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Primary: 11F03
paper · pdf · doi:10.48550/arxiv.1807.10082
openalex publication_date 2018/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we describe how to compute slopes of p-adic L-invariants of arbitrary weight and level by means of the Greenberg-Stevens formula. Our method is based on work of Lauder and Vonk on computing the reverse characteristic series of the Up operator on overconvergent modular forms. Using higher derivatives of this characteristic series, we construct a polynomial whose zeros are precisely the L-invariants appearing in the corresponding space of modular forms with fixed sign of the Atkin-Lehner involution at p. In addition, we describe how to compute this polynomial efficiently. In the final section, we give computational evidence for relations between slopes of L-invariants for small primes.