Expand all Collapse all | Results 1 - 4 of 4 |
1. CMB 2007 (vol 50 pp. 234)
A Remark on a Modular Analogue of the Sato--Tate Conjecture The original Sato--Tate Conjecture concerns the angle distribution
of the eigenvalues arising from non-CM elliptic curves. In this paper,
we formulate a modular analogue of the Sato--Tate Conjecture and prove
that the angles arising from non-CM holomorphic Hecke
eigenforms with non-trivial central characters are not distributed
with respect to the Sate--Tate measure
for non-CM elliptic curves. Furthermore, under a reasonable conjecture,
we prove that the expected distribution is uniform.
Keywords:$L$-functions, Elliptic curves, Sato--Tate Categories:11F03, 11F25 |
2. CMB 2001 (vol 44 pp. 385)
A Hypergraph with Commuting Partial Laplacians Let $F$ be a totally real number field and let $\GL_{n}$ be the
general linear group of rank $n$ over $F$. Let $\mathfrak{p}$
be a prime ideal of $F$ and $F_{\mathfrak{p}}$ the completion of $F$
with respect to the valuation induced by $\mathfrak{p}$. We will
consider a finite quotient of the affine building of the group
$\GL_{n}$ over the field $F_{\mathfrak{p}}$. We will view this object
as a hypergraph and find a set of commuting operators whose sum will
be the usual adjacency operator of the graph underlying the hypergraph.
Keywords:Hecke operators, buildings Categories:11F25, 20F32 |
3. CMB 2001 (vol 44 pp. 282)
Hecke Operators on Jacobi-like Forms Jacobi-like forms for a discrete subgroup $\G \subset \SL(2,\mbb R)$
are formal power series with coefficients in the space of functions on
the Poincar\'e upper half plane satisfying a certain functional
equation, and they correspond to sequences of certain modular forms.
We introduce Hecke operators acting on the space of Jacobi-like forms
and obtain an explicit formula for such an action in terms of modular
forms. We also prove that those Hecke operator actions on Jacobi-like
forms are compatible with the usual Hecke operator actions on modular
forms.
Categories:11F25, 11F12 |
4. CMB 1999 (vol 42 pp. 129)
Hecke Operations and the Adams $E_2$-Term Based on Elliptic Cohomology Hecke operators are used to investigate part of the $\E_2$-term of
the Adams spectral sequence based on elliptic homology. The main
result is a derivation of $\Ext^1$ which combines use of classical
Hecke operators and $p$-adic Hecke operators due to Serre.
Keywords:Adams spectral sequence, elliptic cohomology, Hecke operators Categories:55N20, 55N22, 55T15, 11F11, 11F25 |