Secord-order Cusp Forms and Mixed Mock Modular Forms
نویسندگان
چکیده
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.
منابع مشابه
Eichler-shimura Theory for Mock Modular Forms
We use mock modular forms to compute generating functions for the critical values of modular L-functions, and we answer a generalized form of a question of Kohnen and Zagier by deriving the “extra relation” that is satisfied by even periods of weakly holomorphic cusp forms. To obtain these results we derive an Eichler-Shimura theory for weakly holomorphic modular forms and mock modular forms. T...
متن کاملMIXED MOCK MODULAR q-SERIES
Mixed mock modular forms are functions which lie in the tensor space of mock modular forms and modular forms. As q-hypergeometric series, mixed mock modular forms appear to be much more common than mock theta functions. In this survey, we discuss some of the ways such series arise.
متن کاملAsymptotic bounds for special values of shifted convolution Dirichlet series
In [15], Hoffstein and Hulse defined the shifted convolution series of two cusp forms by “shifting” the usual Rankin-Selberg convolution L-series by a parameter h. We use the theory of harmonic Maass forms to study the behavior in h-aspect of certain values of these series and prove a polynomial bound as h → ∞. Our method relies on a result of Mertens and Ono [22], who showed that these values ...
متن کاملArithmetic Properties of Certain Level One Mock Modular Forms
If k is an integer, we denote by Mk (respectively, Sk) the space of holomorphic modular forms (respectively, cusp forms) of weight k on SL2(Z). Let z ∈ h, the complex upper halfplane, and let q := e. For integers n ≥ 1 and j ≥ 0, define σj(n) := ∑ d|n d , and let Bj denote the jth Bernoulli number. Then the Delta-function and the normalized Eisenstein series for SL2(Z) of even weight k ≥ 2 are ...
متن کاملElliptic Curves , Modular Forms and Related
Nick Andersen (University of California, Los Angeles) Kloosterman sums and Maass cusp forms of half-integral weight ABSTRACT: Kloosterman sums play an important role in modern analytic number theory. I will give a brief survey of what is known about the classical Kloosterman sums and their connection to Maass cusp forms of weight 0. I will then talk about recent progress toward bounding sums of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012