Theta functions, fourth moments of eigenforms and the sup-norm problem II

TY - JOUR

T1 - Theta functions, fourth moments of eigenforms and the sup-norm problem II

AU - Khayutin, Ilya

AU - Nelson, Paul D.

AU - Steiner, Raphael S.

N1 - Publisher Copyright: © The Author(s), 2024. Published by Cambridge University Press.

PY - 2024/5

Y1 - 2024/5

N2 - Let f be an -normalized holomorphic newform of weight k on with N squarefree or, more generally, on any hyperbolic surface attached to an Eichler order of squarefree level in an indefinite quaternion algebra over. Denote by V the hyperbolic volume of said surface. We prove the sup-norm estimate with absolute implied constant. For a cuspidal Maaβ newform of eigenvalue on such a surface, we prove that We establish analogous estimates in the setting of definite quaternion algebras.

AB - Let f be an -normalized holomorphic newform of weight k on with N squarefree or, more generally, on any hyperbolic surface attached to an Eichler order of squarefree level in an indefinite quaternion algebra over. Denote by V the hyperbolic volume of said surface. We prove the sup-norm estimate with absolute implied constant. For a cuspidal Maaβ newform of eigenvalue on such a surface, we prove that We establish analogous estimates in the setting of definite quaternion algebras.

U2 - 10.1017/fmp.2024.9

DO - 10.1017/fmp.2024.9

M3 - Journal article

AN - SCOPUS:85195046538

SN - 2050-5086

VL - 12

JO - Forum of Mathematics, Pi

JF - Forum of Mathematics, Pi

M1 - e11

ER -