Please use this identifier to cite or link to this item: http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/7676
Title: Jacobi forms, Saito-Kurokawa lifts, their Pullbacks and sup-norms on average
Authors: ANAMBY, PRAMATH
Das, Soumya
Dept. of Mathematics
Keywords: Sup-norm
Bergman kernel
Jacobi forms
Saito-Kurokawa lifts
Central values of twisted L-functions
Eichler-Zagier maps
2023-MAR-WEEK3
TOC-MAR-2023
2023
Issue Date: Feb-2023
Publisher: Springer Nature
Citation: Research in the Mathematical Sciences, 10, 14.
Abstract: We formulate a precise conjecture about the size of the L-infinity-mass of the space of Jacobi forms on H-n x C-gxn of matrix index S of size g. This L-infinity-mass is measured by the size of the Bergman kernel of the space. We prove the conjectured lower bound for all such n, g, S and prove the upper bound in the k aspect when n = 1, g >= 1. When n = 1 and g = 1, we make a more refined study of the sizes of the index-(old and) new spaces, the latter via the Waldspurger's formula. Towards this and with independent interest, we prove a power saving asymptotic formula for the averages of the twisted central L-values L(1/2, f (circle times) chi D) with f varying over newforms of level a prime p and even weight k as k, p -> (infinity) and D being (explicitly) polynomially bounded by k, p. Here chi D is a real quadratic Dirichlet character. We also prove that the size of the space of Saito-Kurokawa lifts (of even weight k) is k(5/2) by three different methods (with or without the use of central L-values), and show that the size of their pullbacks to the diagonally embedded HI x H is k(2). In an appendix, the same question is answered for the pullbacks of the whole space S-k(2), the size here being k(3).
URI: https://doi.org/10.1007/s40687-023-00377-z
http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/7676
ISSN: 2522-0144
2197-9847
Appears in Collections:JOURNAL ARTICLES

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