Diophantine quadruples in .
Diophantine representation of generalized Fibonacci numbers.
Diophantine representation of Mersenne and Fermat primes
Diophantine representation of the decimal expansions of and
Diophantine triples with values in binary recurrences
In this paper, we study triples and of distinct positive integers such that and are all three members of the same binary recurrence sequence.
Diophantine undecidability for addition and divisibility in polynomial rings
We prove that the positive-existential theory of addition and divisibility in a ring of polynomials in two variables A[t₁,t₂] over an integral domain A is undecidable and that the universal-existential theory of A[t₁] is undecidable.
Diophantine Undecidability of Holomorphy Rings of Function Fields of Characteristic 0
Let be a one-variable function field over a field of constants of characteristic 0. Let be a holomorphy subring of , not equal to . We prove the following undecidability results for : if is recursive, then Hilbert’s Tenth Problem is undecidable in . In general, there exist such that there is no algorithm to tell whether a polynomial equation with coefficients in has solutions in .
Diophantische Analysis und Modulfunktionen.
Diophantische Approximationen von: Irrationalzahlen mit Kettenbruchnennern von eingeschränktem Wachstum
Diophantische Gleichungen und die universelle Eigenschaft Finslerscher Zahlen.
Diphantine Approximation with Square-free Numbers.
Dirichlet character sums
Dirichlet motives via modular curves
Dirichlet polynomial approximations to zeta functions
Dirichlet polynomials
Dirichlet Series and Gamma Function Associated with Rational Functions
We investigate zeta regularized products of rational functions. As an application, we obtain the asymptotic expansion of the Euler Gamma function associated with a rational function.
Dirichlet series and uniform ergodic theorems for linear operators in Banach spaces
We study the convergence properties of Dirichlet series for a bounded linear operator T in a Banach space X. For an increasing sequence of positive numbers and a sequence of functions analytic in neighborhoods of the spectrum σ(T), the Dirichlet series for is defined by D[f,μ;z](T) = ∑n=0∞ e-μnz fn(T), z∈ ℂ. Moreover, we introduce a family of summation methods called Dirichlet methods and study the ergodic properties of Dirichlet averages for T in the uniform operator topology.
Dirichlet series associated with polynomials
Dirichlet Series Corresponding to Siegel's Modular Forms.
Dirichlet series induced by the Riemann zeta-function
The Riemann zeta-function ζ(s) extends to an outer function in ergodic Hardy spaces on , the infinite-dimensional torus indexed by primes p. This enables us to investigate collectively certain properties of Dirichlet series of the form for in . Among other things, using the Haar measure on for measuring the asymptotic behavior of ζ(s) in the critical strip, we shall prove, in a weak sense, the mean-value theorem for ζ(s), equivalent to the Lindelöf hypothesis.