منابع مشابه
Second order average estimates on local data of cusp forms
We specify sufficient conditions for the square modulus of the local parameters of a family of GLn cusp forms to be bounded on average. These conditions are global in nature and are satisfied for n ≤ 4. As an application, we show that Rankin-Selberg L-functions on GLn1 × GLn2 , for ni ≤ 4, satisfy the standard convexity bound.
متن کاملAutomorphic forms of higher order and convolution of L - series of cusp forms Anton
In this paper a theory of Hecke operators for higher order modular forms is established. The definition of cusp forms and attached L-functions is extended beyond the realm of parabolic invariants. The role of representation theoretic methods is clarified and, motivated by higher order forms, new convolution products of L-functions are introduced.
متن کاملThe Classification of Higher-order Cusp Forms
In this paper we establish the complete classification of cusp forms of all orders. Higher-order cusp forms constitute a natural extension of the notion of classical cusp forms and they have attracted the interest of several researchers in the broader area of automorphic forms during the last few years. Reasons for this interest include its relevance for new approaches to problems related to th...
متن کاملSecord-order Cusp Forms and Mixed Mock Modular Forms
In this paper, we consider the space of second order cusp forms. We determine that this space is precisely the same as a certain subspace of mixed mock modular forms. Based upon Poincaré series of Diamantis and O’Sullivan [21] which span the space of second order cusp forms, we construct Poincaré series which span a natural (more general) subspace of mixed mock modular forms.
متن کاملNonvanishing of L-functions of Cusp Forms inside the Critical Strip
A theorem of W. Kohnen states that the generalized Riemann hypothesis (GRH) holds on an average for holomorphic cusp forms on the upper half plane for the full modular group SL2(Z). In this article we prove a couple of generalizations of this theorem of Kohnen that the GRH holds on an average for holomorphic cusp forms on the upper half plane for arbitrary level, weight and primitive nebentypus...
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ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2006
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-006-0147-2