Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Power series expansions of modular forms and their interpolation
  properties   Let x be a CM point on a modular or Shimura curve and p a prime of good
reduction, split in the CM field K. We define an expansion of an holomorphic
modular form f in the p-adic neighborhood of x and show that the expansion
coefficients give information on the p-adic ring of definition of f. Also, we
show that letting x vary in its Galois orbit, the expansions coefficients allow
to construct a p-adic measure whose moments squared are essentially the values
at the centre of symmetry of L-functions of the automorphic representation
attached to f based-changed to K and twisted by a suitable family of
Grossencharakters for K.

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The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc