Zero-density estimate for modular form L-functions in weight aspect
Bob Hough (2012)
Acta Arithmetica
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Displaying similar documents to “Modular case of Levinson's theorem”
Zero-density estimate for modular form L-functions in weight aspect
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Vincent Bosser (2008)
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Wissam Raji (2007)
Acta Arithmetica
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Primitive Points on a Modular Hyperbola
Igor E. Shparlinski (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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For positive integers m, U and V, we obtain an asymptotic formula for the number of integer points (u,v) ∈ [1,U] × [1,V] which belong to the modular hyperbola uv ≡ 1 (mod m) and also have gcd(u,v) =1, which are also known as primitive points. Such points have a nice geometric interpretation as points on the modular hyperbola which are "visible" from the origin.
A converse theorem for second-order modular forms of level N
Özlem Imamoglu, Yves Martin (2006)
Acta Arithmetica
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Karen Taylor (2012)
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Acta Arithmetica
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Shinji Fukuhara (2012)
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Numerical calculation of twisted adjoint -values attached to modular forms.
Hiraoka, Yoshio (2000)
Experimental Mathematics
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Modular equations for some η-products
(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.