On the Siegel modular function field of degree three
On the Siegel-Tatuzawa theorem
On the Siegel-Tatuzawa-Hoffstein theorem
On the Sign Changes of (...(x) - lix). II.
On the simultaneous approximation of , and
On the simultaneous approximation of certain numbers.
On the simultaneous diophantine approximation of values of certain algebraic functions
On the simultaneous diophantine approximation of values of certain hypergeometric and algebraic functions
On the singular Drinfeld modules of rank 2.
On the singular set, the resolvent and Fermi's Golden Rule for finite volume hyperbolic surfaces.
On the singularities of multiple L-functions
We investigate the singularities of a class of multiple L-functions considered by Akiyama and Ishikawa [2].
On the size of dissociated bases.
On the size of integer solutions of elliptic equations, II
On the size of L(1,χ) and S. Chowla's hypothesis implying that L(1,χ) > 0 for s > 0 and for real characters χ
We give explicit constants κ such that if χ is a real non-principal Dirichlet character for which L(1,χ) ≤ κ, then Chowla's hypothesis is not satisfied and we cannot use Chowla's method for proving that L(s,χ) > 0 for s > 0. These constants are larger than the previous ones κ = 1- log 2 = 0.306... and κ = 0.367... we obtained elsewhere.
On the size of prime factors of integers
On the size of the first factor of the class number of a cyclotomic field.
On the size of zeros of quadratic forms over rational function fields.
On the slopes of the operator acting on overconvergent modular forms
We show that the slopes of the operator acting on 5-adic overconvergent modular forms of weight with primitive Dirichlet character of conductor 25 are given by eitherdepending on and .We also prove that the space of classical cusp forms of weight and character has a basis of eigenforms for the Hecke operators and which is defined over .
On the smallest pseudopower
On the smallest solution to the general binary quadratic diophantine equation