Related papers: On ordinary forms and ordinary Galois representati…
We comment on a recent paper by Chaichian et al. (Phys.Rev.Lett. 71(1993)3405).
We report on observations we made on computational data that suggest a generalization of Maeda's conjecture regarding the number of Galois orbits of newforms of level $N = 1$, to higher levels. They also suggest a possible formula for this…
The classification of the representations of the generalized deformed oscillator algebra is given together with several comments about possibility of introducing a coproduct structure in some type of deformed oscillator algebra.
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
The goal of this work is to formulate a systematical method for looking for the simple closed form or continued fraction representation of a class of rational series. As applications, we obtain the continued fraction representations for the…
In this article, we realize some groups as Galois groups over rational numbers and finite extension of rational numbers by studying right splitting of some exact sequences, Galois correspondence and algebraic operations on Galois…
This paper collects many results on galoisian ideals and Galois theory.
We introduce a complex q-Fourier transform as a generalization of the (real) one analyzed in [Milan J. Math. {\bf 76} (2008) 307]. By recourse to tempered ultradistributions we show that this complex plane-generalization overcomes all…
In this paper we study a group theoretical generalization of the well-known Gauss's formula that uses the generalized Euler's totient function introduced in [11].
In this paper, we study extra-twists for automorphic representations of $\mathrm{GL}_n$ and use them to give a precise description of the image of the Galois representations associated with regular algebraic cuspidal automorphic…
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
Using a new presentation for partition algebras (J. Algebraic Combin. 37(3):401-454, 2013), we derive explicit combinatorial formulae for the seminormal representations of the partition algebras. These results generalise to the partition…
This unpublished paper is a copy (completed by a development of section 5 and by minor corrections) of the article with the same title published in: Complex Analysis and Digital Geometry, Proceedings from the Kiselmanfest, 2006, Acta…
The subject of this paper is a simulation to that in [1] but here we consider substitutions corresponding to transpositions instead of replacements.
The authors provide a survey of certain aspects of their joint work with the late M. K. Vamanamurthy. Most of the results are simple to state and deal with special functions, a topic of research where S. Ramanujan's contributions are…
The present article is devoted to representations of rational numbers in terms sign-variable Cantor expansions. The main attention is given to one of the discussions given by J. Galambos in [4].
An important step in the proof of the Herman invariant tori conjecture was the introduction of a normal form with poles along the resonance loci, replacing the Birkhoff normal form, which we call the Hamiltonian normal form. This paper is…
We give a description of the rational representations of the differential Galois group of a Picard-Vessiot extension.
We prove in some cases a formula for the Greenberg-Benois $\mathcal{L}$-invariant of the spin, standard and adjoint Galois representations associated with Siegel-Hilbert modular forms. In order to simplify the calculation, we give a new…
We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.