Zeta integrals for GSp(4) via Bessel models

Abstract

To my parents I owe more than I can possibly express. Without their love, blessings and sacrifices I would probably not have succeeded in carrying through the project. Finally, I would like to dedicate this work to my children Finn and Harper, who have been the greatest motivation for me to pursue my career. v

Newforms of Saito-Kurokawa lifts

“…Now i) of the lemma is obvious by (2.10), and ii) follows from i) and the computation of Piatetski-Shapiro and Soudry [14]. According to Table 5 of [24],…”

“…also defines a L-function, which is called the regular part of L(s, π), and denoted by L reg (s, π). By the argument in p. 466 of [24], the ratio…”

“…Let A 2 and N 2 denote the diagonals and the unipotent radicals of P 2 respectively. The Jacquet-Waldspurger module V N,Λ of V defined in [24] is obtained by replacing N G with N in (2.3).…”

Rankin–selberg Integrals for Local Symmetric Square Factors on Gl(2)

“…In the spirit of [33], we define exceptional L ‐functions in such a way that exceptional poles can be regular but precisely if there exist exceptional poles. Definition We let where s 0 is taken over all exceptional poles of .…”

“…The terminologies of “exceptional” and “regular” parts of L ‐functions have been extensively exploited in the construction of L ‐functions for . We refer to [33] and the references therein, which are all based on the work of Piatetski‐Shapiro [31]. The method of good sections was reshaped and rapidly developed in the perspective of the doubling method [13, 43].…”