An analogue of the Thue-Morse sequence.
An analogue of the Weierstrass ζ-function in characteristic p
An analogue of the Weil representation for G2.
An analysis of GCD and LCM matrices via the -factorization.
An analytic construction of degenerating curves over complete local rings
An analytic function and iterated integrals
An annihilator for the -Selmer group by means of Heegner points
Let be a modular elliptic curve, and let be an imaginary quadratic field. We show that the -Selmer group of over certain finite anticyclotomic extensions of , modulo the universal norms, is annihilated by the «characteristic ideal» of the universal norms modulo the Heegner points. We also extend this result to the anticyclotomic -extension of . This refines in the current contest a result of [1].
An Apéry-like difference equation for Catalan's constant.
An application of a formula of Western to the evaluation of certain Jacobsthal sums
An application of a lower bound for linear forms in two logarithms to the Terai-Jeśmanowicz conjecture
An Application of a Theorem of Deuring and Safarevic.
An application of Banach algebra techniques for multiplicative functions.
An application of Catalan numbers on Cayley tree of order 2: Single polygon counting.
An application of dihedral fields to representations of primes by binary quadratic forms
An application of Hilbert's irreducibility theorem to diophantine equations
An application of Kloosterman sums
An application of Kronecker's theorem to transcendence theory.
An application of Mellin-Barnes' type integrals to the mean square of Lerch zeta-functions.
We shall establish full asymptotic expansions for the mean squares of Lerch zeta-functions, based on F. V. Atkinson's device. Mellin-Barnes' type integral expression for an infinite double sum will play a central role in the derivation of our main formulae.
An application of Mellin-Barnes type integrals to the mean square of Lerch zeta-functions (II).
For the Lerch zeta-function Φ(s,x,λ) defined below, the multiple mean square of the form (1.1), together with its discrete and Irbid analogues, (1.2) and (1.3) are investigated by means of Atkinson's [2] dissection method applied to the product Φ(u,x,λ)Φ(υ,x,-λ), where u and υ are independent complex variables (see (4.2)). A complete asymptotic expansion of (1.1) as Im s → ±∞ is deduced from Theorem 1, while those of (1.2) and (1.3) as q → ∞ and (at the same time) as Im s → ±∞ are deduced from Theorems...
An application of metric diophantine approximation in hyperbolic space to quadratic forms.
For any real τ, a lim sup set WG,y(τ) of τ-(well)-approximable points is defined for discrete groups G acting on the Poincaré model of hyperbolic space. Here y is a 'distinguished point' on the sphere at infinity whose orbit under G corresponds to the rationals (which can be regarded as the orbit of the point at infinity under the modular group) in the classical theory of diophantine approximation.In this paper the Hausdorff dimension of the set WG,y(τ) is determined for geometrically finite groups...