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Integral mean values of L-functions.

Zhang, Qiao.

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Integral mean values of L-functions.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Integral mean values of L-functions./
Author:	Zhang, Qiao.
Description:	56 p.
Notes:	Adviser: Dorian Goldfeld.
Contained By:	Dissertation Abstracts International64-04B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3088459

Integral mean values of L-functions.
Zhang, Qiao.

Integral mean values of L-functions. - 56 p.

Adviser: Dorian Goldfeld.

Thesis (Ph.D.)--Columbia University, 2003.

Let <italic>f</italic> ∈ <math> <f> <sc>S<inf><mit>k</mit></inf></sc></f> </math>(Γ<sub>0</sub>(<italic>N</italic>)) be a cusp form of weight <italic> k</italic> and level <italic>N</italic>, and <italic>L</italic>(<italic>s, f</italic>) its normalized <italic>L</italic>-function. This paper is devoted to the investigation of the integral mean values for <italic>L</italic>(<italic> s, f</italic>) along the critical line <math> <f> <sc><ge>R<mit>s</mit></ge></sc></f> </math> = &half;, and obtains an asymptotic formula in the case that the level <italic>N</italic> is squarefree. A theory of nonholomorphic Poincaré series for GL(2, <math> <f> <blkbd>R</blkbd></f> </math>) is developed. Further generalizations to non-squarefree levels and to Maass forms are also indicated.Subjects--Topical Terms:

515831
Mathematics.

Integral mean values of L-functions.
LDR:01583nam 2200253 a 45 001 937705
005 20110511
008 110511s2003 eng d
035 $a (UnM)AAI3088459
035 $a AAI3088459
040 $a UnM $c UnM
100 1 $a Zhang, Qiao. $3 1261563
245 1 0 $a Integral mean values of L-functions.
300 $a 56 p.
500 $a Adviser: Dorian Goldfeld.
500 $a Source: Dissertation Abstracts International, Volume: 64-04, Section: B, page: 1763.
502 $a Thesis (Ph.D.)--Columbia University, 2003.
520 $a Let <italic>f</italic> ∈ <math> <f> <sc>S<inf><mit>k</mit></inf></sc></f> </math>(Γ<sub>0</sub>(<italic>N</italic>)) be a cusp form of weight <italic> k</italic> and level <italic>N</italic>, and <italic>L</italic>(<italic>s, f</italic>) its normalized <italic>L</italic>-function. This paper is devoted to the investigation of the integral mean values for <italic>L</italic>(<italic> s, f</italic>) along the critical line <math> <f> <sc><ge>R<mit>s</mit></ge></sc></f> </math> = &half;, and obtains an asymptotic formula in the case that the level <italic>N</italic> is squarefree. A theory of nonholomorphic Poincaré series for GL(2, <math> <f> <blkbd>R</blkbd></f> </math>) is developed. Further generalizations to non-squarefree levels and to Maass forms are also indicated.
590 $a School code: 0054.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 0 $a Columbia University. $3 571054
773 0 $t Dissertation Abstracts International $g 64-04B.
790 $a 0054
790 1 0 $a Goldfeld, Dorian, $e advisor
791 $a Ph.D.
792 $a 2003
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3088459