Arithmetic cycles on Picard modular surfaces and modular forms of Nebentypus.

J.W. Cogdell

Displaying similar documents to “Arithmetic cycles on Picard modular surfaces and modular forms of Nebentypus.”

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Modular equations for some η-products

(2013)

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The classical modular equations involve bivariate polynomials that can be seen to be univariate in the modular invariant j with integer coefficients. Kiepert found modular equations relating some η-quotients and the Weber functions γ₂ and γ₃. In the present work, we extend this idea to double η-quotients and characterize all the parameters leading to this kind of equation. We give some properties of these equations, explain how to compute them and give numerical examples.

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Differential overconvergence

Alexandru Buium, Arnab Saha (2011)

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We prove that some of the basic differential functions appearing in the (unramified) theory of arithmetic differential equations, especially some of the basic differential modular forms in that theory, arise from a "ramified situation". This property can be viewed as a special kind of overconvergence property. One can also go in the opposite direction by using differential functions that arise in a ramified situation to construct "new" (unramified) differential functions.