The thermodynamics of interacting vortices constricted to move in one-dimensional tracks carved out on superconducting films in the extreme type-II limit is mapped into the Coulomb gas model of random matrices. Application of the Selberg Integral supply exact expressions for the constitutive relation for two configurations of tracks. PACS number: 74.20.Hi, 02.10.Sp To appear in J. Phys. Cond. M...

using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of hammerstein type . the mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). the procedure of this method is so fast and don't need high cpu and complicated programming. the advantages of this method are that we can applied for those integral equation...

We prove explicit rationality-results for Asai- $L$-functions, $L^S(s,\Pi',{\rm As}^\pm)$, and Rankin-Selberg $L^S(s,\Pi\times\Pi')$, over arbitrary CM-fields $F$, relating critical values to powers of $(2\pi i)$. Besides determining the contribution archimedean zeta-integrals our formulas as concrete i)$, it is one advantages approach, that applies very general non-cuspidal isobaric automorphi...

Abstract In this paper, we prove the Gan-Gross-Prasad conjecture and Ichino-Ikeda for unitary groups $U_{n}\times U_{n+1}$ U n × + 1 in all endoscopic cases. Our main technical innovation is compu...

We establish a new equivalent condition for the Grand Riemann Hypothesis L-functions in wide subclass of Selberg class terms canonical systems differential equations. A system is determined by real symmetric matrix-valued function called Hamiltonian. To condition, we use an inverse problem special type.

For cofinite Kleinian groups, with finite-dimensional unitary representations, we derive the Selberg trace formula. As an application we define the corresponding Selberg zeta-function and compute its divisor, thus generalizing results of Elstrodt, Grunewald and Mennicke to non-trivial unitary representations. We show that the presence of cuspidal elliptic elements sometimes adds ramification po...

We study a model sifting problem introduced by Selberg, in which all of the primes have roughly the same size. We show that the Selberg lower bound sieve is asymptotically optimal in this setting, and we use this to give a new lower bound on the sifting limit βκ in terms of the sifting dimension κ. We also show that one can use a rounding procedure to improve on the Selberg lower bound sieve by...

New types of relationships between Feynman integrals are presented. It is shown that Feynman integrals satisfy functional equations connecting integrals with different values of scalar invariants and masses. A method is proposed for obtaining such relations. The derivation of functional equations for one-loop propagatorand vertex type integrals is given. It is shown that a propagator type integ...

Such identities arise in Rankin-Selberg integral representations of L-functions. For GL2, a naive, direct computation is sufficient. However, for general GLn and other higher-rank groups, direct computation is inadequate. Further, connecting local Rankin-Selberg computations to Schur functions usefully connects these computations to the Shintani-Casselman-Shalika formulas for spherical p-adic W...