Real quadratic singular moduli and \(p\)-adic families of modular forms

DOI10.1007/978-3-031-52163-8_9MaRDI QIDQ6611640

Paulina Fust, Alice Pozzi, Mafalda Santos, Hanneke Wiersema, Judith Ludwig

Publication date: 27 September 2024

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Congruences for modular and (p)-adic modular forms (11F33) (p)-adic theory, local fields (11F85) Holomorphic modular forms of integral weight (11F11) Arithmetic aspects of modular and Shimura varieties (11G18) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Rigid analytic geometry (14G22)

Cites Work

• Hilbert modular forms and the Gross-Stark conjecture
• Heegner points and derivatives of \(L\)-series
• A modular construction of unramified p-extensions of \(\mathbb{Q}(\mu_p)\)
• \(p\)-adic Banach spaces and families of modular forms
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• Real quadratic Borcherds products
• Diagonal restrictions of \(p\)-adic Eisenstein families
• The rationality of Stark-Heegner points over genus fields of real quadratic fields
• Lectures on formal and rigid geometry
• Efficient calculation of Stark-Heegner points via overconvergent modular symbols
• Elliptic units for real quadratic fields
• Singular moduli for real quadratic fields: a rigid analytic approach
• On the modularity of elliptic curves over \(\mathbb Q\): wild 3-adic exercises
• FINITENESS OF $ E(\mathbf{Q})$ AND $ \textrm{Ø}(E,\mathbf{Q})$ FOR A SUBCLASS OF WEIL CURVES
• Projections of 𝐶^{∞} automorphic forms
• LISSITÉ DE LA COURBE DE HECKE DE $\mathrm{GL}_2$ AUX POINTS EISENSTEIN CRITIQUES
• Integration on \({\mathcal H_p}\times\mathcal H\) and arithmetic applications.
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