Harder’s conjecture and Miyawaki lift
Abstract
Abstract Let k , j {k,j} and n be positive integers such that k is odd, and both j and n are even, satisfying j ≡ n mod 4 {j\equiv n~{}\operatorname{mod}\,4} . Let f and g be primitive forms of weight 2 k + j - 2 {2k+j-2} and k + j / 2 - n / 2 - 1 {k+j/2-n/2-1} , respectively, for SL 2 ( ℤ ) {{\mathrm{SL}}_{2}({\mathbb{Z}})} . Then we propose a conjecture on the congruence between the Klingen–Eisenstein lift of the Miyawaki lift of f and g of type II and a certain lift of a vector-valued Hecke eigenform of weight ( k + j , k ) {(k+j,k)} for Sp 2 ( ℤ ) {\mathrm{Sp}_{2}({\mathbb{Z}})} . This conjecture implies Harder’s conjecture. Through this formulation, we prove Harder’s conjecture in some cases.
Fields of Study & Subjects
Advanced Algebra and Geometry
Analytic Number Theory Research
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Forum Mathematicum
- Volume
- 38
- Issue
- 4
- Pages
- 1111–1137
- Publication date
- 1 January 2026
- Language
- EN