A note on simultaneous nonvanishing twists
نویسندگان
چکیده
منابع مشابه
A Note on Twists of (y^2=x^3+1)
‎‎In the category of Mordell curves (E_D:y^2=x^3+D) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (E_1), ‎and of the generic rank at least two and at least three as cubic twists of (E_1). ‎Previous work‎, ‎in the category of Mordell curves with trivial torsion groups‎, ‎has found infinitely many elliptic curves with ...
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in the category of mordell curves (e_d:y^2=x^3+d) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (e_1), and of the generic rank at least two and at least three as cubic twists of (e_1). previous work, in the category of mordell curves with trivial torsion groups, has found infinitely many elliptic curves with rank at least seven as sextic tw...
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Let f be a newform of even weight k, level M and character ψ and let g be a newform of even weight l, level N and character η. We give a generalization of a theorem of Elliott, regarding the average values of Dirichlet L-functions, in the context of twisted modular L-functions associated to f and g. Using this result, we find a lower bound in terms of Q for the number of primitive Dirichlet cha...
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If d is square-free or is a fundamental discriminant, then let χd = χD denote the Kronecker character for the quadratic field Q( √ d) whose fundamental discriminant is D. Throughout D shall denote a fundamental discriminant. The D-quadratic twist of F , denoted F ⊗ χD, is the newform corresponding to the twist of F by the character χD. In particular, if gcd(M,D) = 1, then (F ⊗ χD)(z) = ∑∞ n=1 χ...
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Let Sn(ψ1, . . . , ψn) denote the set of simultaneously (ψ1, . . . , ψn)–approximable points in Rn and S∗ n (ψ) denote the set of multiplicatively ψ–approximable points in Rn. Let M be a manifold in Rn. The aim is to develop a metric theory for the sets M∩Sn(ψ1, . . . , ψn) and M∩S∗ n (ψ) analogous to the classical theory in whichM is simply Rn. In this note, we mainly restrict our attention to...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2012
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2011.09.004