Expand all Collapse all | Results 201 - 205 of 205 |
201. CMB 1997 (vol 40 pp. 364)
On the non-vanishing of a certain class of Dirichlet series In this paper,
we consider Dirichlet series with Euler products of the form
$F(s) = \prod_{p}{\bigl(1 + {a_p\over{p^s}}\bigr)}$ in $\Re(s) > 1$,
and which are regular in $\Re(s) \geq 1$ except for a pole of
order $m$ at $s = 1$.
We establish criteria for such a Dirichlet series to be non-vanishing
on the line of convergence. We also show that our results
can be applied to yield non-vanishing results for a subclass of the
Selberg class and the Sato-Tate conjecture.
Categories:11Mxx, 11M41 |
202. CMB 1997 (vol 40 pp. 376)
The dual pair $PGL_3 \times G_2$ Let $H$ be the split, adjoint group of type $E_6$ over a $p$-adic field.
In this paper we study the restriction of the minimal representation of
$H$ to the closed subgroup $PGL_3 \times G_2$.
Categories:22E35, and, 50, 11F70 |
203. CMB 1997 (vol 40 pp. 214)
Polynomials of quadratic type producing strings of primes The primary purpose of this paper is to provide necessary and
sufficient conditions for certain quadratic polynomials of negative
discriminant (which we call Euler-Rabinowitsch type), to produce
consecutive prime values for an initial range of input values less than
a Minkowski bound. This not only generalizes the classical work of
Frobenius, the later developments by Hendy, and the generalizations by
others, but also concludes the line of reasoning by providing a
complete list of all such prime-producing polynomials, under the
assumption of the generalized Riemann hypothesis ($\GRH$). We demonstrate
how this prime-production phenomenon is related to the exponent of the
class group of the underlying complex quadratic field. Numerous
examples, and a remaining conjecture, are also given.
Categories:11R11, 11R09, 11R29 |
204. CMB 1997 (vol 40 pp. 72)
Generalized Siegel modular forms and cohomology of locally symmetric varieties We generalize Siegel modular forms and construct an exact sequence
for the cohomology of locally symmetric varieties which plays the
role of the Eichler-Shimura isomorphism for such generalized Siegel
modular forms.
Categories:11F46, 11F75, 22E40 |
205. CMB 1997 (vol 40 pp. 81)
Une caractÃ©risation des corps satisfaisant le thÃ©orÃ¨me de l'axe principal Resum\'e. On caract\'erise les corps $K$ satisfaisant le th\'eor\`eme
de l'axe principal \`a l'aide de propri\'et\'es des formes
carac\-t\'erisation de ces m\^emes corps due \`a Waterhouse,
on retrouve \`a partir de l\`a, de fa\c{c}on \'el\'ementaire,
un r\'esultat de Becker selon lequel un pro-$2$-groupe qui se
r\'ealise comme groupe de Galois absolu d'un tel corps $K$ est
engendr\'e par des involutions.
ABSTRACT. We characterize general fields $K$, satisfying the
Principal Axis Theorem, by means of properties of trace forms of
the finite extensions of $K$. From this and Waterhouse's
characterization of the same fields, we rediscover, in quite an
elementary way, a result of Becker according to which a
pro-$2$-group which occurs as the absolute Galois group of such
a field $K$, is generated by
Categories:11E10, 12D15 |