2,912 research outputs found
Sign changes of coefficients of half integral weight modular forms
For a half integral weight modular form we study the signs of the Fourier
coefficients . If is a Hecke eigenform of level with real
Nebentypus character, and is a fixed square-free positive integer with
, we show that for all but finitely many primes the sequence
has infinitely many signs changes. Moreover, we prove
similar (partly conditional) results for arbitrary cusp forms which are not
necessarily Hecke eigenforms
Non-vanishing of -functions associated to cusp forms of half-integral weight
In this article, we prove non-vanishing results for -functions associated
to holomorphic cusp forms of half-integral weight on average (over an
orthogonal basis of Hecke eigenforms). This extends a result of W. Kohnen to
forms of half-integral weight.Comment: 8 pages, Accepted for publication in Oman conference proceedings
(Springer
Locally harmonic Maass forms and the kernel of the Shintani lift
In this paper we define a new type of modular object and construct explicit
examples of such functions. Our functions are closely related to cusp forms
constructed by Zagier which played an important role in the construction by
Kohnen and Zagier of a kernel function for the Shimura and Shintani lifts
between half-integral and integral weight cusp forms. Although our functions
share many properties in common with harmonic weak Maass forms, they also have
some properties which strikingly contrast those exhibited by harmonic weak
Maass forms. As a first application of the new theory developed in this paper,
one obtains a new perspective on the fact that the even periods of Zagier's
cusp forms are rational as an easy corollary
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