Automorphic functions on SL(m,ℝ)

One presents a method for the expansion of functions F:SL(m,)^h that are automorphic with respect ot the congruence subgroup in SL(m,). For m=2 the method gives the usual expansion into Fourier series. One gives a comparison with the expansion presented previously by the author in the paper: The expansion of automorphic functions, J. Sov. Math.,26, No. 3 (1984).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 129, pp. 164–176, 1983.     

Automorphic functions and the Bass-Milnor-Serre homomorphism,I

Let v=[exp2i/3], let q=(3) be an ideal in v and let SL_m(v,q) be the congruence subgroup modq in SL_m(v). For the solution of the congruence subgroup problem, Bass, Milnor, and Serre have constructed (making use of the properties of the symbol of cubic residue) a homomorphism :SL_m(v,q)^*. We consider here as a system of multipliers. The fundamental object of investigation is the Eisenstein series on SL₃()/Su(3) automorphic relative to SL₃(v,q) with the system of multipliers . For this Eisenstein series one has computed certain coefficients of the expansion with respect to the basis indicated in the author's paper: The expansion of automorphic functions on SL₃()/Su(3), Zap. Nauchn. Sem. LOMI, Vol. 125, pp. 144–153, 1983.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 129, pp. 85–126, 1983.     

On ∗-representations of deformations of canonical anticommutation relations

We consider irreducible ∗-representations of deformations of canonical anticommutation relations (CAR) that belong to the class of ∗-algebras generated by generalized quons.     

Stability of the C *-Algebra Associated with Twisted CCR

The universal enveloping C ^*-algebra A of twisted canonical commutation relations is considered. It is shown that, for any (–1,1), the C ^*-algebra A is isomorphic to the C ^*-algebra A ₀ generated by partial isometries t _i ,t _i ^*,i=1,¨,d satisfying the relations t _i ^* t _j = _ij (1– _k<i t _k t _k ^*), t _j t _i =0, ij and it is proved that the Fock representation of A is faithful.     

Cosmological production of vector bosons and cosmic microwave background radiation

An intensive cosmological production of vector W and Z bosons is considered within a cosmological model that involves a relative scale of measurement. Field-theory models are studied in which cosmic microwave background radiation and baryon matter may appear as products of the decay of such primordial bosons.     

Stability of a Special Class of $$q_{ij}$$ -CCR and Extensions of Higher-Dimensional Noncommutative Tori

The -algebras A_{{q i}}, generated by generalised quon commutation relations are considered. The nuclearity of these algebras is proved. It is shown that A_{{q i}}, is isomorphic to the extension of a higher-dimensional noncommutative torus. Irreducible representations of A_{{q i}}, are considered. It is shown that the Fock representation is faithful.     

Tuning magnetotransport through a magnetic kink crystal in a chiral helimagnet

We consider magnetotransport properties in a conducting chiral helimagnet, where the magnetic kink crystal (MKC) is formed under weak magnetic field applied perpendicular to the helical axis. The MKC behaves as a magnetic superlattice potential and results in Bragg scattering of conduction electrons. Tuning of the weak magnetic field enables us to control the size of the superlattice Brillouin zone and gives rise to a series of divergent resistivity anomalies originating from resonant Bragg scatterings. We discuss as well a nontrivial magnetic structure in the resonant states realized in the subsystem of the itinerant electrons.     

Computing the values of <Emphasis Type="Italic">L</Emphasis>-functions,and the chebyshev polynomials

The Chebyshev polynomials and Chebyshev’s economization method are applied to speed up the computation of the values of L-functions. Bibliography: 3 titles.