
Weak Siegel-Weil formula for đť•„â‚‚(â„š) and arithmetic on quaternions
Author(s) -
Tuoping Du
Publication year - 2021
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/tran/8324
Subject(s) - algorithm , artificial intelligence , computer science
We prove a weak version of the Siegel-Weil formula on SL 2 \operatorname {SL}_2 for the dual pair ( SL 2 , O 2 , 2 ) (\operatorname {SL}_2, O_{2, 2}) , where O 2 , 2 O_{2, 2} is the split orthogonal group. By this formula and the Siegel-Weil formula, we give explicit formulas for Hecke correspondence’s degree and average representation numbers over genus associated to Eichler orders. At last, we give explicit formulas for representations of a number as sums of three squares and four squares by local Whittaker functions, and it turns out that these functions are exactly the local factors of Hardy’s singular series.