location:  Publications → journals
Search results

Search: MSC category 11F25 ( Hecke-Petersson operators, differential operators (one variable) )

 Expand all        Collapse all Results 1 - 4 of 4

1. CMB 2007 (vol 50 pp. 234)

Kuo, Wentang
 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--TateCategories:11F03, 11F25

2. CMB 2001 (vol 44 pp. 385)

Ballantine, Cristina M.
 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, buildingsCategories:11F25, 20F32

3. CMB 2001 (vol 44 pp. 282)

Lee, Min Ho; Myung, Hyo Chul
 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)

Baker, Andrew
 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 operatorsCategories:55N20, 55N22, 55T15, 11F11, 11F25