Heights of Heegner points on Shimura curves.
Heights of varieties in multiprojective spaces and arithmetic Nullstellensätze
We present bounds for the degree and the height of the polynomials arising in some problems in effective algebraic geometry including the implicitization of rational maps and the effective Nullstellensatz over a variety. Our treatment is based on arithmetic intersection theory in products of projective spaces and extends to the arithmetic setting constructions and results due to Jelonek. A key role is played by the notion of canonical mixed height of a multiprojective variety. We study this notion...
Heuristics on Tate-Shafarevitch groups of elliptic curves defined over .
Hida families, -adic heights, and derivatives
This paper concerns the arithmetic of certain -adic families of elliptic modular forms. We relate, using a formula of Rubin, some Iwasawa-theoretic aspects of the three items in the title of this paper. In particular, we examine several conjectures, three of which assert the non-triviality of an Euler system, a -adic regulator, and the derivative of a -adic -function. We investigate sufficient conditions for the first conjecture to hold and show that, under additional assumptions, the first...
High rank eliptic curves of the form y2 = x3 + Bx.
Seven elliptic curves of the form y2 = x3 + B x and having rank at least 8 are presented. To find them we use the double descent method of Tate. In particular we prove that the curve with B = 14752493461692 has rank exactly 8.
Higher dimensional Dedekind sums in function fields
Higher Mahler measures and zeta functions
Higher order operations in Deligne cohomology.
Higher regulators and Hecke L-series of imaginary quadratic fields I.
Hilbert sets and zeta functions over finite fields.
Hodge modules on Shimura varieties and their higher direct images in the Baily–Borel compactification
Höhentheorie (mit einem Appendix von Jürg Kramer: Eine alternative Begründung der Néron-Tate Höhe).
Horizontal Factorizations of Certain Hasse-Weil Zeta Functions - a Remark on a Paper by Taniyama
Hyperelliptic modular curves
Hyperelliptic modular curves X₀*(N) with square-free levels