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 Ramanujan's identities. - Generalized Rademacher functions and some congruence properties. Language: English