V. V. Zudilin, “On the irrationality of values of the zeta-function,” in: Reports of the 23d Conference of Young Scientists (Moscow State University, 9–14 April, 2001 ) [in Russian], Moscow, 2001 (to appear), in: E-print math.NT/0104249....
This chapter discusses the application of mean values of the Riemann zeta-function to the distribution of zeros. The precise results about the horizontal distribution of the zeros of the Riemann zeta-function are deduced from mean value ... JB Conrey,A Ghosh,SM Gonek - 《Number Theory Trace...
The authors prove that ζ ˜(s) can be meromorphically continued to the whole complex plane, and evaluate explicitly the values of this zeta-function at non-positive integers in terms of Bernoulli numbers. It turns out that ζ ˜(-m)∈ for m∈, m≥0....
Fig. 8.2 Bode plot of control-to-output transfer function predicted by the model of Fig.8.1, with analytical expressions for the important features 电路分析(步骤中的第4步)中通常遇到的困难是模型的复杂性:实际电路中可能包含数百个元件,因此对其分析可能会导致复杂的推导,棘手的方程式以及可能出现大量的代...
In this paper, we shall define the renormalization of the multiple q-zeta values (MqZV) which are special values of multiple q-zeta functions ζ q (s 1, ..., s d ) when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang...
With additional assumptions, we prove that the special values of the partial zeta functions at s = 0 are given by a quasi-polynomial of degree less than or equal to d as a function of n. We apply this to conclude that the special values of the Hecke's L-functions at s = 0 for ...
After τ(ρ) is found for given values of n and l,χ(ρ) can be obtained using Eq. (20). Finally, the complete unnormalized radial wavefunction is Яn,l = χ(ζr)/r. Therefore, the normalized radial wavefunctions are given by the following equation: $$ {{R}}_{{n,l}} \...
Special values of zeta functions attached to Siegel modular forms 1981 PB - Société mathématique de France VL - 14 IS - 1 SP - 77 EP - 120 LA - eng KW - Siegelmodular forms; Dirichlet series; arithmetic properties Zbl0389.10023MR58 #21950; [3] WL BAILYJr., On the Theory of θ...
We calculate special values of Witten L-functions for SU(2) and SU(3). We prove some algebraicity for such special values. Moreover, we prove that such values turn out to be zero in many cases. These are generalizations of classical results due to Euler for the Riemann zeta function.Pre...
We study multiple zeta values (MZVs) from the viewpoint of zeta-functions associated with the root systems which we have studied in our previous papers. In fact, the $r$-ple zeta-functions of Euler-Zagier type can be regarded as the zeta-function associated with a certain sub-root system...