The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros has been recently generalized onto subharmonic functions with the Riesz measure on a half-line in Rn, n≥3. Here we extend ...The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros has been recently generalized onto subharmonic functions with the Riesz measure on a half-line in Rn, n≥3. Here we extend the Drasin complement to the Valiron-Titchmarsh theorem and show that if u is a subharmonic function of this class and of order 0〈ρ〈1, then the existence of the limit limr→∞logu(r)/N(r), where N(r) is the integrated counting function of the masses of u, implies the regular asymptotic behavior for both u and its associated measure.展开更多
In this note we establish two theorems concerning asymptotic expansion of Riemann-Siegel integrals as well as formula of generating function (double series) of coefficents of that expansion (for computation aims);...In this note we establish two theorems concerning asymptotic expansion of Riemann-Siegel integrals as well as formula of generating function (double series) of coefficents of that expansion (for computation aims); we also discuss similar results for Dirichlet series (L(s, fh) and L(s, X)), with m odd integer and X ( n ) (mod( m ) ) (even) primitive characters ( inappendix B ) .展开更多
文摘The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros has been recently generalized onto subharmonic functions with the Riesz measure on a half-line in Rn, n≥3. Here we extend the Drasin complement to the Valiron-Titchmarsh theorem and show that if u is a subharmonic function of this class and of order 0〈ρ〈1, then the existence of the limit limr→∞logu(r)/N(r), where N(r) is the integrated counting function of the masses of u, implies the regular asymptotic behavior for both u and its associated measure.
文摘In this note we establish two theorems concerning asymptotic expansion of Riemann-Siegel integrals as well as formula of generating function (double series) of coefficents of that expansion (for computation aims); we also discuss similar results for Dirichlet series (L(s, fh) and L(s, X)), with m odd integer and X ( n ) (mod( m ) ) (even) primitive characters ( inappendix B ) .