An orthogonal test of the L-functions Ratios Conjecture, II
Analytic and combinatoric aspects of Hurwitz polyzêtas
In this work, a symbolic encoding of generalized Di-richlet generating series is found thanks to combinatorial techniques of noncommutative rational power series. This enables to explicit periodic generalized Dirichlet generating series – particularly the coloured polyzêtas – as linear combinations of Hurwitz polyzêtas. Moreover, the noncommutative version of the convolution theorem gives easily rise to an integral representation of Hurwitz polyzêtas. This representation enables us to build the...
Analytic continuation of multiple zeta-functions and their values at non-positive integers
Analytic continuation of representations and estimates of automorphic forms.
Analytic properties of zeta functions and subgroup growth.
Approximations to -logarithms and -dilogarithms, with applications to -zeta values.
ARI/GARI, la dimorphie et l'arithmétique des multizêtas : un premier bilan
Nous tentons, dans ce survol, de présenter une structure méconnue : l'algèbre de Lie ARI et son groupe GARI. Puis nous montrons quels progrès elle a déjà permis de réaliser dans l'étude arithmético-algébrique des valeurs zêta multiples et aussi quelles possibilités elle ouvre pour l'exploration du phénomène plus général de /emph{dimorphie numérique}.
Artin formalism and heat kernels.
Asymptotic Estimates on Finite Abelian Groups
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.
Block additive functions on the Gaussian integers
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.
Certain mean values and non-vanishing of automorphic L-functions with large level
Circles passing through five or more integer points
We find an improvement to Huxley and Konyagin’s current lower bound for the number of circles passing through five integer points. We conjecture that the improved lower bound is the asymptotic formula for the number of circles passing through five integer points. We generalise the result to circles passing through more than five integer points, giving the main theorem in terms of cyclic polygons with m integer point vertices. Theorem. Let m ≥ 4 be a fixed integer. Let be the number of cyclic polygons...
Combinatorial aspects of multiple zeta values.