scholarly journals Topological modular forms with level structure

2015 ◽  
Vol 203 (2) ◽  
pp. 359-416 ◽  
Author(s):  
Michael Hill ◽  
Tyler Lawson
Keyword(s):  
Modular Forms ◽  
Level Structure ◽  
Topological Modular Forms

scholarly journals The Picard group of topological modular forms via descent theory

2016 ◽  
Vol 20 (6) ◽  
pp. 3133-3217 ◽  
Author(s):  
Akhil Mathew ◽  
Vesna Stojanoska
Keyword(s):  
Modular Forms ◽  
Picard Group ◽  
Descent Theory ◽  
Topological Modular Forms

scholarly journals Power series expansions of modular forms and p-adic interpolation of the square roots of Rankin–Selberg special values

2021 ◽  
pp. 1-41
Author(s):  
Andrea Mori
Keyword(s):  
Power Series ◽  
Modular Forms ◽  
Level Structure ◽  
Automorphic Representation ◽  
Base Change ◽  
Series Expansions ◽  
Square Roots ◽  
Infinite Type ◽  
Special Values ◽  
Power Series Expansions

Let [Formula: see text] be a newform of even weight [Formula: see text] for [Formula: see text], where [Formula: see text] is a possibly split indefinite quaternion algebra over [Formula: see text]. Let [Formula: see text] be a quadratic imaginary field splitting [Formula: see text] and [Formula: see text] an odd prime split in [Formula: see text]. We extend our theory of [Formula: see text]-adic measures attached to the power series expansions of [Formula: see text] around the Galois orbit of the CM point corresponding to an embedding [Formula: see text] to forms with any nebentypus and to [Formula: see text] dividing the level of [Formula: see text]. For the latter we restrict our considerations to CM points corresponding to test objects endowed with an arithmetic [Formula: see text]-level structure. Also, we restrict these [Formula: see text]-adic measures to [Formula: see text] and compute the corresponding Euler factor in the formula for the [Formula: see text]-adic interpolation of the “square roots”of the Rankin–Selberg special values [Formula: see text], where [Formula: see text] is the base change to [Formula: see text] of the automorphic representation of [Formula: see text] associated, up to Jacquet-Langland correspondence, to [Formula: see text] and [Formula: see text] is a compatible family of grössencharacters of [Formula: see text] with infinite type [Formula: see text].

scholarly journals Topological Modular Forms of Level 3

2009 ◽  
Vol 5 (2) ◽  
pp. 853-872 ◽  
Author(s):  
Mark Mahowald ◽  
Charles Rezk
Keyword(s):  
Modular Forms ◽  
Topological Modular Forms ◽  
Level 3

scholarly journals On the ring of cooperations for 2‐primary connective topological modular forms

2019 ◽  
Vol 12 (2) ◽  
pp. 577-657 ◽  
Author(s):  
M. Behrens ◽  
K. Ormsby ◽  
N. Stapleton ◽  
V. Stojanoska
Keyword(s):  
Modular Forms ◽  
Topological Modular Forms

scholarly journals Secondary invariants for string bordism and topological modular forms

2014 ◽  
Vol 138 (8) ◽  
pp. 912-970 ◽  
Author(s):  
Ulrich Bunke ◽  
Niko Naumann
Keyword(s):  
Modular Forms ◽  
Topological Modular Forms
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