The points of a certain fivefold over finite fields and the twelfth power of the eta function

DOI10.1006/ffta.2001.0315zbMath1026.11053OpenAlexW2056957410MaRDI QIDQ1604414

Scott Ahlgren

Publication date: 4 July 2002

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/ffta.2001.0315

zbMATH Keywords

elliptic curvesHecke operatorEichler-Selberg trace formulaweight 6 modular form

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) Dedekind eta function, Dedekind sums (11F20) (n)-folds ((n>4)) (14J40)

Related Items

Modularity of two double covers of \(\mathbb{P}^5\) branched along 12 hyperplanes, Generalized Paley graphs and their complete subgraphs of orders three and four, Sato-Tate distribution of \(p\)-adic hypergeometric functions, Trace formulas for Hecke operators, Gaussian hypergeometric functions, and the modularity of a threefold, Elliptic Calabi-Yau fivefolds and 2d (0,2) F-theory landscape, Sequences, modular forms and cellular integrals, Hypergeometric functions over finite fields and modular forms. A survey and new conjectures, Hypergeometric functions over ${\mathbb {F}_p}$ and relations to elliptic curves and modular forms, On the trace formula for Hecke operators on congruence subgroups. II, Traces of Hecke operators in level 1 and Gaussian hypergeometric functions, Traces of Hecke operators in level 1 and \(p\)-adic hypergeometric functions, Traces of Hecke operators and refined weight enumerators of Reed-Solomon codes

Cites Work

• Nonsingular plane cubic curves over finite fields
• On the geometry and arithmetic of some Siegel modular threefolds
• Modularity of a certain Calabi-Yau threefold
• The \(L\)-series of certain rigid Calabi-Yau threefolds
• Explicit formula of the traces of Hecke operators for \(\Gamma_0(N)\)
• Sur la lacunarité des puissances de η
• The basis problem for modular forms on Γ₀(𝑁)
• Representation of primes by the principal form of discriminant -D when the classnumber h(-D) is 3
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