Titlebook: Galois Theory and Modular Forms; Ki-ichiro Hashimoto,Katsuya Miyake,Hiroaki Nakamur Book 2004 Kluwer Academic Publishers 2004 Abelian vari

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The Arithmetic of Weierstrass Points on Modular Curves ,, (,)imes .. We begin with some generalities; most of these can be found, for example, in the book of Farkas and Kra [F-K]. Suppose that . is a compact Riemann surface of genus . ≥2. If γ is a positive integer, then let .. (.) denote the space of holomorphic r-differentials on .. Each .. (.) is a finite-

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Semistable Abelian Varieties with Small Division Fieldsson of the local factors ([And], [Seri]), it also predicts that the L-series of an abelian surface defined over ? should be the L-series of a Hecke eigen cusp form of weight 2 on a suitable group commensurable with Sp. (?). The only decisive examples are related to lifts of automorphic representatio

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Q-curves with Rational ,-invariants and Jacobian Surfaces of GL,-typees over .. We discuss their minimality as .-curves, and the classification, as well as the Neben type characters of the associated modular forms. This can be described as the sign change phenomenon by guar-tic twists of curves over .. We also study their 2-fold covers by genus two curves. Among othe

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Points Defined over Cyclic Quartic Extensions on an Elliptic Curve and Generalized Kummer Surfaces.,is a finitely generated abelian group. We fix . once and for all, and we study the behavior of the rank of the group . as . varies through a certain family. We are particularly interested in the family .. (.) of all Galois extensions . whose Galois group Gal(./.) is isomorphic to a prescribed fini

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On Quadratic Number Fields Each Having an Unramified Extension Which Properly Contains the Hilbert Cs the Hilbert class field of its genus field (in the wide sense). The motivation of this study is the author’s observation that under the Generalized Riemann Hypothesis (GRH), for most quadratic number fields of small conductors, their maximal unramified extensions coincide with the Hilbert class fi

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Distribution of units of an algebraic number fieldrested in their distribution. For an integral ideal n of ., we set . and . which is equal to the extension degree of the ramified part of the ray class field corresponding to the ideal n over . Let . be a Galois extension of the rational number field ., which contains the field ., and fix an element

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Akkreditierung als Mikropolitikar group PSL.(..) as Galois group over ? in the case 144169 is non-square modulo .. Recently, this result was widely extended by Reverter-Vila [16] and Dieulefait-Vila [3]. Moreover, studying the Jacobian of a plane curve of genus 2, Mestre [13] showed that the field generated by the .-division poin