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Showing 1 to 5 of 5 for “"Zagier"”.
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A numerical investigation of Apéry-like recursions and related Picard-Fuchs equations
… at 2 and 3. It is a continuation of the work of Zagier , who considered generalization of the first equation and numerically investigated it. The study is made for two generalizations of the second equation, one used the mirror symmetry idea from the theory of Calabi-Yau varieties and another …
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Arithmetic of Maass forms of half-integral weight
… quadratic fields, expanding on the work of Zagier and Duke-Imamoglu-Toth. Next, we examine the deep relationship between sums of Kloosterman sums and Maass cusp forms, motivated by work of Kuznetsov and Sarnak-Tsimerman, among others. Finally, we focus on the classical mock theta functions …
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The asymptotic behavior of the integer solutions of the Rosenberger equations
… is the Markoff equation, x2 + y2 + z2 = 3xyz. Zagier investigated the asymptotic behavior of the integer solutions of the Markoff equation. In this paper, we apply Zagier's techniques to the Rosenberger equations and show that the number N(T) of positive integer solutions that are bounded by T …
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p-adic Heights of Heegner points on Shimura curves
… variety A associated to f. This p-adic Gross-Zagier formula generalises the result obtained by Perrin-Riou when F=Q and N satisfies the so-called Heegner condition. We deduce applications to both the p-adic and the classical Birch and Swinnerton-Dyer conjectures for A.
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Self-intersection of Manin-Drinfeld Cycles and Taylor expansion of L-functions
… along this philosophy was achieved by Gross and Zagier, who proved that the derivative of the L-function of an elliptic curve is equal, up to a constant, to the Néron-Tate height pairing of a special point called a Heegner point on the elliptic curve. A more recent result was proven in the …