Modular equations for some η-products

• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11G18: Arithmetic aspects of modular and Shimura varieties
• 14G35: Modular and Shimura varieties
• 11F03: Modular and automorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 161
• Numer: 4
• Strony: 301-326

Daty

wydano

2013

Twórcy

Identyfikatory

DOI

10.4064/aa161-4-1