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....
2882 accesses explore all metrics abstract we construct a large family of fourier interpolation bases for functions analytic in a strip symmetric about the real line. interesting examples involve the nontrivial zeros of the riemann zeta function and other l -functions. we establish a duality principl...
Sec. 5, Conjecture]. In fact, both zeta functions are related to a probability: the former to the probability of generating a profinite groupGwithrandom elements, the latter to the probability⟦⟧⟦⟧. However, it is important to remark that Mann’s zeta function is not known to ex...
To keep the discussion as concrete as possible, we shall focus on so-called Apéry-like formulae for special values of the Riemann Zeta function. Many of these results are apparently new, and much more work needs to be done before they can be formally proved and properly classified....
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...
Here, g3/2(⋅) is the standard Bose integral, ζ(⋅) is the Riemann zeta function, and NT is the number of atoms in the thermal component. Note that for a non-interacting gas in the thermodynamic limit, the number of thermal atoms is simply NTid=ζ(3)(kBT/ℏω¯)3=ηTN,...
1, blue survival function). The second involves increasing lifespan, such that mortality reaches M at higher values of T. In this case, survival rates decline more slowly, increasing the probability of living beyond T (Fig. 1, yellow survival function). Fig. 1: Survival functions under ...
ZETA FUNCTIONS OF A CLASS OF ELLIPTIC CURVES OVER A RATIONAL FUNCTION FIELD OF CHARACTERISTIC TWO ERNST-ULRICH GEKELER, RITA LEITL, AND BODO WACK Abstract. We show how to calculate the zeta functions and the orders |X| of Tate-Shafarevich groups of the elliptic curves with equation Y 2 + ...
new estimates on the additive energy of zeroes of the Riemann zeta function. We are hoping that the ANTEDB will receive more contributions in the future, for instance expanding to other types of exponents, or to update the database as new results are obtained (or old ones added). In the...
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...