2023/11/26 by Chung-Hang Kwan, Chung‐Hang Kwan, Kwan, Chung-Hang
Mathematics · #Analytic Number Theory Research #Advanced Algebra and Geometry #Finite Group Theory Research
paper · pdf · doi:10.1007/s00208-024-02914-9
Abstract This is a sequel to our previous articles (Kwan in Algebra Number Theory. arXiv:2112.08568v4 ; Kwan in Spectral moment formulae for GL(3)× GL(2) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>G</mml:mi> <mml:mi>L</mml:mi> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>)</mml:mo> <mml:mo>×</mml:mo> <mml:mi>G</mml:mi> <mml:mi>L</mml:mi> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> L -functions II: Eisenstein case, 2023. arXiv:2310.09419 ). In this work, we apply recent techniques that fall under the banner of ‘Period Reciprocity’ to study moments of GL(3)× GL(2) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>G</mml:mi> <mml:mi>L</mml:mi> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>)</mml:mo> <mml:mo>×</mml:mo> <mml:mi>G</mml:mi> <mml:mi>L</mml:mi> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> L -functions in the non-archimedean aspects, with a view towards the ‘Twisted Moment Conjectures’ formulated by CFKRS.