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There is reason to expe
t that the 2k-th moment of the Riemann zeta
fun
tion
an be related to the spe
tral theory of GL(k) or GL(2k). The work
of Motohashi [27℄ supports the idea of seeki...
Automorphic forms are generalizations of periodic functions; they are functions on a group that
are invariant under a discrete subgroup. A natural way to arrange this invariance is by averaging.
Eis...
WZ-proofs of "divergent" Ramanujan-type series
Hypergeometric series WZ-method Ramanujan-type series for 1/ and 1/2 Barnes Integrals
2011/1/21
We prove some ”divergent” Ramanujan-type series for 1/ and 1/2 applying a Barnes-integrals strategy of the WZ-method.
The Peano-Baker series
The Peano-Baker series math
2010/11/12
This note reviews the Peano-Baker series and its use to solve the general linear system of ODEs. The account is elementary and self-contained, and is meant as a pedagogic introduction to this approac...
Local properties of Hilbert spaces of Dirichlet series
Local properties Hilbert spaces Dirichlet series
2010/11/19
We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet series defined using these as weights. This ex...
Eisenstein Series, Alternative Modular Bases and Approximations of $1/\pi$
Eisenstein Series Alternative Modular Bases
2010/11/22
In this article using the theory of Eisenstein series, we give rise to the complete evaluation of two Gauss hypergeometric functions. Moreover we evaluate the modulus of each of these functions and t...
Geometric motivic Poincaré series of quasi-ordinary singularities
Geometric motivic Poincaré series quasi-ordinary singularities
2010/11/19
The geometric motivic Poincar\'e series of a germ $(S,0)$ of complex algebraic variety takes into account the classes in the Grothendieck ring of the jets of arcs through $(S,0)$. Denef and Loeser pro...
Horizontal visibility graphs: exact results for random time series
Horizontal visibility graphs random time series
2010/4/2
The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows to apply methods of complex network theory for characterizing time se...