An Asymptotic Series for an Additive Divisor Problem.
An asymptotic series for the mean value of Dirichlet L-functions.
An average form of Artin's conjecture
An average formula for the class number
An awful problem about integers in base four
An axiomatization of Nesterenko's method and applications on Mahler functions II
An effective Bertini theorem and the number of rational points of a normal complete intersection over a finite field
An effective bound of p for algebraic points on Shimura curves of Γ₀(p)-type
In previous articles, we showed that for number fields in a certain large class, there are at most elliptic points on a Shimura curve of Γ₀(p)-type for every sufficiently large prime number p. In this article, we obtain an effective bound for such p.
An effective estimate for the density of zeros of Hecke-Landau zeta-functions
An effective lower bound for a certain exponential function
An effective lower bound for the height of algebraic numbers
An effective order of Hecke-Landau zeta functions near the line σ=1, II (some applications)
An effective order of Hecke-Landau zeta functions near the line σ = 1. I
An effective p-adic analogue of a theorem of Thue
An effective p-adic analogue of a theorem of Thue II. The greatest prime factor of a binary form
An effective p-adic analogue of a theorem of Thue III. The diophantine equation
An effective procedure for minimal bases of ideals in Z[x]
We give an effective procedure to find minimal bases for ideals of the ring of polynomials over the integers.
An effective proof of the hyperelliptic Shafarevich conjecture
Let be a hyperelliptic curve of genus over a number field with good reduction outside a finite set of places of . We prove that has a Weierstrass model over the ring of integers of with height effectively bounded only in terms of , and . In particular, we obtain that for any given number field , finite set of places of and integer one can in principle determine the set of -isomorphism classes of hyperelliptic curves over of genus with good reduction outside .
An effective result of André-Oort type II
We prove some new effective results of André-Oort type. In particular, we state certain uniform improvements of the main result in [L. Kühne, Ann. of Math. 176 (2012), 651-671]. We also show that the equation X + Y = 1 has no solution in singular moduli. As a by-product, we indicate a simple trick rendering André's proof of the André-Oort conjecture effective. A significantly new aspect is the usage of both the Siegel-Tatuzawa theorem and the weak effective lower bound on the class number of an...
An effective Shafarevich theorem for elliptic curves