Results 1 to 10 of about 1,090,342 (306)
Proceedings of the Edinburgh Mathematical Society, 1962 Letandbe, respectively, the upper and lower central series of a group G. Our purpose in this note is to extend known results and find some information as to which of the factors Zk/Zk−1 and Γk/Γk+1 may be infinite. Though our conclusions about the lower central series will be quite general we assume in the other case that the group is f.n., i.e.
I. D. Macdonald
openalex +3 more sources
On the Central Derivative of Hecke L-Series [PDF]
Journal of Number Theory, 2000 Let \(p\equiv 3\pmod 4\) be a prime number such that \(p>3\) and let \(k\geq 0\) be an integer. Let \(L(s,\mu)\) be the Hecke \(L\)-series of \(E={\mathbb Q}(\sqrt{-p})\) associated with a canonical Hecke character \(\mu\) of weight \(k\). When the root number (=\((2/p)(-1)^k\)) of \(\mu\) is \(-1\), the central special value \(L(1,\mu)\) is ...
Tonghai Yang
openalex +2 more sources
A note on inverse central factorial series [PDF]
Proceedings of the Edinburgh Mathematical Society, 1946 The purpose of this brief note is to draw attention to a type of inverse factorial series which, so far as the writer can judge, has not been intensively studied. The central difference formulae of interpolation and the corresponding infinite series in central factorial polynomials have in the past received much attention, and so also has the ordinary ...
A. C. Aitken
openalex +3 more sources
On the moments of Hecke series at central points
Functiones et Approximatio Commentarii Mathematici, 2002 Asymptotic formulas for $\sum_{ _j\le K} _j H_j^k(1/2)$ are proved when $k = 3,4$, where $H_j(s)$ is the Hecke series.
Aleksandar Ivić
openalex +6 more sources
On the moments of Hecke series at central points. II [PDF]
Functiones et Approximatio Commentarii Mathematici, 2003 16 pages, TeX formatting ...
Aleksandar Ivić, Matti Jutila
openalex +5 more sources
The upper central series in soluble groups [PDF]
Illinois Journal of Mathematics, 1961 K. W. Gruenberg
openalex +5 more sources
The twelfth moment of central values of Hecke series
Journal of Number Theory, 2004 The author proves the bound \[ \sum_{\kappa_j\leq K}\alpha_j H^{12}_j({{1\over2}}) \ll_\varepsilon K^{4+\varepsilon},\leqno(1) \] which may be viewed as the analogue of \textit{D. R. Heath-Brown}'s estimate [Q. J. Math., Oxf. (2) 29, 443--462 (1978; Zbl 0394.10020)] \[ \int_0^T| \zeta({\textstyle{1\over2}}+it)| ^{12}\text{ d}t \ll_\varepsilon T^{2 ...
Matti Jutila
openalex +4 more sources
On exponential sums with Hecke series at central points [PDF]
Functiones et Approximatio Commentarii Mathematici, 2007 Upper bound estimates for the exponential sum $$ \sum_ ...
Aleksandar Ivić
openalex +5 more sources
On the central limit theorem for lacunary trigonometric series [PDF]
Tohoku Mathematical Journal, 1968 Shigeru Takahashi
openalex +5 more sources
A version of the central limit theorem for trigonometric series [PDF]
Tohoku Mathematical Journal, 1964 Shigeru Takahashi
openalex +4 more sources