Blomer, V. and Harcos, Gergely and Michel, P. and Mao, Z. (2007) A Burgesslike subconvex bound for twisted Lfunctions. Forum Mathematicum, 19 (1). pp. 61105. ISSN 09337741 (print), 14355337 (online)

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Abstract
Let g be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus, X a primitive character of conductor q, and s a point on the critical line Rs = 1/2. It is proved that L(g circle times chi, s) << epsilon,g,s q(1/2(1/8)(120)+epsilon), where epsilon > 0 is arbitrary and theta = 7/64 is the current known approximation towards the RamannJanPetersson conjecture (which would allow theta = 0); moreover, the dependence on s and all the parameters of g is polynomial. This result is an analog of Burgess' classical subconvex bound for Dirichlet Lfunctions. In Appendix 2 the above result is combined with a theorem of Waldspurger and the adelic calculations of BaruchMao to yield an improved uniform upper bound for the Fourier coefficients of holomorphic halfintegral weight cusp forms.
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA71 Number theory / számelmélet 
Depositing User:  Erika Bilicsi 
Date Deposited:  18 Dec 2012 16:03 
Last Modified:  18 Dec 2012 16:03 
URI:  http://real.mtak.hu/id/eprint/3630 
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