Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Publication Type
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Topics On The Spectral Theory Of Automorphic Forms, Dustin David Belt
Topics On The Spectral Theory Of Automorphic Forms, Dustin David Belt
Theses and Dissertations
We study the analytic properties of the Eisenstein Series of $frac {1}{2}$-integral weight associated with the Hecke congruence subgroup $Gamma_0(4)$. Using these properties we obtain asymptotics for sums of certain Dirichlet $L$-series. We also obtain a formula reducing the study of Selberg's Eigenvalue Conjecture to the study of the nonvanishing of the Eisenstein Series $E(z,s)$ for Hecke congruence subgroups $Gamma_0(N)$ at $s=frac {1+i}{2}$.
Numerical Approximation To Ζ(2n+1), Tian-Xiao He, Michael Dancs
Numerical Approximation To Ζ(2n+1), Tian-Xiao He, Michael Dancs
Scholarship
In this short paper, we establish a family of rapidly converging series expansions ζ(2n +1) by discretizing an integral representation given by Cvijovic and Klinowski [3] in Integral representations of the Riemann zeta function for odd-integer arguments, J. Comput. Appl. Math. 142 (2002) 435–439. The proofs are elementary, using basic properties of the Bernoulli polynomials.
Numerical Approximation To Ζ(2n+1), Tian-Xiao He, Michael J. Dancs
Numerical Approximation To Ζ(2n+1), Tian-Xiao He, Michael J. Dancs
Tian-Xiao He
In this short paper, we establish a family of rapidly converging series expansions ζ(2n +1) by discretizing an integral representation given by Cvijovic and Klinowski [3] in Integral representations of the Riemann zeta function for odd-integer arguments, J. Comput. Appl. Math. 142 (2002) 435–439. The proofs are elementary, using basic properties of the Bernoulli polynomials.