Modular forms of genus 2 and weight 1.
Rainer Weissauer (1992)
Mathematische Zeitschrift
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Rainer Weissauer (1992)
Mathematische Zeitschrift
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Daeyeol Jeon, Chang Heon Kim (2007)
Acta Arithmetica
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Dohoon Choi, YoungJu Choie, Toshiyuki Kikuta (2013)
Acta Arithmetica
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Suppose that f is an elliptic modular form with integral coefficients. Sturm obtained bounds for a nonnegative integer n such that every Fourier coefficient of f vanishes modulo a prime p if the first n Fourier coefficients of f are zero modulo p. In the present note, we study analogues of Sturm's bounds for Siegel modular forms of genus 2. As an application, we study congruences involving an analogue of Atkin's U(p)-operator for the Fourier coefficients of Siegel modular forms of genus...
Bruce Hunt (1990)
Compositio Mathematica
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Josep Gonzalez Rovira (1991)
Annales de l'institut Fourier
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We compute, in a unified way, the equations of all hyperelliptic modular curves. The main tool is provided by a class of modular functions introduced by Newman in 1957. The method uses the action of the hyperelliptic involution on the cusps.
Heima Hayashi (2006)
Acta Arithmetica
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D. Choi (2006)
Acta Arithmetica
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Francesc Bars, Aristides Kontogeorgis, Xavier Xarles (2013)
Acta Arithmetica
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We determine all modular curves X(N) (with N ≥ 7) that are hyperelliptic or bielliptic. We also give a proof that the automorphism group of X(N) is PSL₂(ℤ/Nℤ), whence it coincides with the normalizer of Γ(N) in PSL₂(ℝ) modulo ±Γ(N).
Besser, Amnon (1997)
Documenta Mathematica
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(2013)
Acta Arithmetica
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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.
Hidegoro Nakano (1968)
Studia Mathematica
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Chang Heon Kim, Ja Kyung Koo (1998)
Acta Arithmetica
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We find a generator of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.
Daeyeol Jeon, Euisung Park (2005)
Acta Arithmetica
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