Title | Galois Theory and Modular Forms [electronic resource] / edited by Ki-ichiro Hashimoto, Katsuya Miyake, Hiroaki Nakamura |
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Imprint | Boston, MA : Springer US, 2004 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-0249-0 |
Descript | XII, 394 p. online resource |
I. Arithmetic geometry -- The arithmetic of Weierstrass points on modular curves X0(p) -- Semistable abelian varieties with small division fields -- Q-curves with rational j-invariants and jacobian surfaces of GL2-type -- Points defined over cyclic quartic extensions on an elliptic curve and generalized Kummer surfaces -- The absolute anabelian geometry of hyperbolic curves -- II. Galois groups and Galois extensions -- Regular Galois realizations of PSL2(p2) over ?(T) -- Middle convolution and Galois realizations -- On the essential dimension of p-groups -- Explicit constructions of generic polynomials for some elementary groups -- On dihedral extensions and Frobenius extensions -- On the non-existence of certain Galois extensions -- Frobenius modules and Galois groups -- III. Algebraic number theory -- On quadratic number fields each having an unramified extension which properly contains the Hilbert class field of its genus field -- Distribution of units of an algebraic number field -- On capitulation problem for 3-manifolds -- On the Iwasawa ?-invariant of the cyclotomic ?p-extension of certain quartic fields -- IV. Modular forms and arithmetic functions -- Quasimodular solutions of a differential equation of hypergeometric type -- Special values of the standard zeta functions -- p-adic properties of values of the modular j-function -- Thompson series and Ramanujanโs identities -- Generalized Rademacher functions and some congruence properties