The q-Mellin transform of automorphic forms and converse theorems
نویسندگان
چکیده
منابع مشابه
Completely q - multiplicative functions : the Mellin transform approach
(1.1) f(aq + b) = f(aq) + f(b) or f(aq + b) = f(aq)f(b) for all r ≥ 0, a ≥ 0 and 0 ≤ b < q. Note that these equations force f(0) = 0 or f(0) = 1 respectively. These functions are called q-additive and q-multiplicative, respectively. It is easy to see that the functional equations imply that these functions are defined for all integers, when the values f(aq) are known for 1 ≤ a ≤ q − 1 and all r...
متن کاملThe Twisted Mellin Transform
The “twisted Mellin transform” is a slightly modified version of the usual classical Mellin transform on L([0,∞)). In this short note we investigate some of its basic properties. From the point of view of combinatorics one of its most interesting properties is that it intertwines the differential operator, df/dx, with its finite difference analogue, ∇f = f(x)−f(x−1). From the point of view of a...
متن کاملAutomorphic Forms
We apply a theorem of J. Lurie to produce cohomology theories associated to certain Shimura varieties of type U(1, n−1). These cohomology theories of topological automorphic forms (TAF ) are related to Shimura varieties in the same way that TMF is related to the moduli space of elliptic curves. We study the cohomology operations on these theories, and relate them to certain Hecke algebras. We c...
متن کاملDirichlet series from automorphic forms
This integral trick assumes greater significance when the function f is known to have strong decay properties both at 0 and at ∞, since then the Mellin transform is entire in s. One way to ensure such rapid decay is via eigenfunction properties in the context of automorphic forms. [2] • The archetype Mellin transform: zeta from theta • Abstracting to holomorphic modular forms • Variation: wavef...
متن کاملQuaternionic Fourier-Mellin Transform
In this contribution we generalize the classical Fourier Mellin transform [3], which transforms functions f representing, e.g., a gray level image defined over a compact set of R. The quaternionic Fourier Mellin transform (QFMT) applies to functions f : R → H, for which |f | is summable over R+ × S under the measure dθ dr r . R ∗ + is the multiplicative group of positive and non-zero real numbe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2008
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa132-2-5