Asymptotic mean square of the product of the Riemann zeta-function and a Dirichlet polynomial.
Asymptotic nature of higher Mahler measure
We consider Akatsuka’s zeta Mahler measure as a generating function of the higher Mahler measure of a polynomial where is the integral of over the complex unit circle. Restricting ourselves to P(x) = x - r with |r| = 1 we show some new asymptotic results regarding , in particular as k → ∞.
Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values
We present asymptotic representations for certain reciprocal sums of Fibonacci numbers and of Lucas numbers as a parameter tends to a critical value. As limiting cases of our results, we obtain Euler’s formulas for values of zeta functions.
Asymptotics of counts of small components in random structures and models of coagulation-fragmentation
We establish necessary and sufficient conditions for the convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. The multiplicative measures depict distributions of component spectra of random structures and also the equilibria of classic models of statistical mechanics and stochastic processes of coagulation-fragmentation. We show that the convergence of multiplicative measures is equivalent to the asymptotic independence of counts of...
Asymptotische Entwicklung von verallgemeinerten Bernoullischen Funktionen und von Teilsummen Dirichletscher Reihen mit periodischer Koeffizientenfolge.
Average distributions and products of special values of L-series
Averages of twisted elliptic L-functions
Bartholdi zeta functions for hypergraphs.
Basilejský problém devětkrát jinak
V tomto článku podrobně rozebereme celkem devět řešení tzv. basilejského problému (hledání součtu převrácených hodnot druhých mocnin přirozených čísel). První publikované řešení od L. Eulera využívá rozkladu ``nekonečného polynomu'' na součin kořenových činitelů. Druhé řešení pracuje s Taylorovým rozvojem funkce arkussinus a rekurentním vzorcem pro jistý určitý integrál, třetí je založeno na vztazích mezi goniometrickými funkcemi a exponenciálou a výpočtu limity s využitím l'Hospitalova pravidla....
Beiträge zur Theorie der Riemannschen Zetafunktion
Benford's law, values of L-functions and the 3x+1 problem
Bethe ansatz, inverse scattering transform and tropical Riemann theta function in a periodic soliton cellular automaton for .
Block additive functions on the Gaussian integers
Borwein and Bradley's Apéry-like formulae for .
Bounding L-functions by class numbers
Bounds for automorphic L-functions.
Bounds for automorphic L-functions. II.
Bounds for double zeta-functions
In this paper we shall derive the order of magnitude for the double zeta-functionof Euler-Zagier type in the region .First we prepare the Euler-Maclaurinsummation formula in a suitable form for our purpose, and then we apply the theory of doubleexponential sums of van der Corput’s type.
Bounds for zeta and related functions.
Cartan Bernoulli Numbers as Values of L-Series.