Use this URL to cite or link to this record in EThOS:  https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.560391 
Title:  Eigenforms of halfintegral weight  
Author:  Purkait, Soma 
ISNI:
0000 0004 2726 3441


Awarding Body:  University of Warwick  
Current Institution:  University of Warwick  
Date of Award:  2012  
Availability of Full Text: 


Abstract:  
Let k be an odd integer and N a positive integer such that 4  N. Let X be a Dirichlet character modulo N. Shimura decomposes the space of halfintegral weight forms Sk/2(N,X) as Sk/2(N,X) = S0(N,X)oOΦSk/2(N,X,Φ) where Φ runs through the newforms of weight k1 and level dividing N/2 and character X2; Sk/2(N,X,Φ) is the subspace of forms that are Shimuraequivalent to Φ; and S0(N,X) is the subspace generated by singlevariable thetaseries. We give an explicit algorithm for computing this decomposition. Once we have the decomposition, we can exploreWaldspurger's theorem expressing the critical values of the Lfunctions of twists of an elliptic curve in terms of the coefficients of modular forms of halfintegral weight. Following Tunnell, this often allows us to give a criterion for the nth twist of an elliptic curve to have positive rank in terms of the number of representations of certain integers by certain ternary quadratic forms.


Supervisor:  Not available  Sponsor:  University of Warwick  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.560391  DOI:  Not available  
Keywords:  QA Mathematics  
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