On \(L\)-functions of modular elliptic curves and certain \(K3\) surfaces

DOI10.1007/s11139-021-00388-wzbMath1502.11044arXiv2007.09803OpenAlexW3147770438MaRDI QIDQ2115270

Letong Hong, Malik Amir

Publication date: 15 March 2022

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.09803

zbMATH Keywords

elliptic curves\(L\)-functionsmodular formsLehmer's conjecture\(K3\) surfacesLucas sequences

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Holomorphic modular forms of integral weight (11F11) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items

Even values of Ramanujan's tau-function, A short note on inadmissible coefficients of weight 2 and \(2k+1\) newforms, Variants of Lehmer's speculation for newforms

Uses Software

• Magma
• PARI/GP
• SageMath
• LMFDB
• GitHub

Cites Work

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• On the practical solution of the Thue equation
• Solving Thue equations of high degree
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• The Magma algebra system. I: The user language
• On elliptic modular surfaces
• The vanishing of Ramanujan's function \(\tau(n)\)
• Existence of primitive divisors of Lucas and Lehmer numbers
• The Arithmetic of Elliptic Curves
• Odd values of the Ramanujan $\tau$-function
• Zeta functions of an infinite family of K3 surfaces
• Modular Forms
• Multiplicative 𝜂-quotients