Modular forms arising from zeta functions in two variables attached to prehomogeneous vector spaces related to quadratic forms

DOI10.1017/S0027763000008874zbMath1075.11042MaRDI QIDQ4652213

Takahiko Ueno

Publication date: 24 February 2005

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

modular forms for \(\Gamma_0(N)\)prehomogeneous vector spacesWeil's converse theoremzeta functions of several variablesQuadratic forms

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Prehomogeneous vector spaces (11S90)

Related Items (6)

Shintani correspondence for Maass forms of level \(N\) and prehomogeneous zeta functions ⋮ The modularity of Siegel's zeta functions ⋮ On serial posets with positive-definite quadratic Tits form. ⋮ The fundamental theorem of prehomogeneous vector spaces modulo $p^m$ (With an appendix by F. Sato) ⋮ Dirichlet series of two variables, real analytic Jacobi-Eisenstein series of matrix index, and Katok-Sarnak type result ⋮ Converse theorems for automorphic distributions and Maass forms of level \(N\)

Cites Work

• Sums involving the values at negative integers of \(L\)-functions of quadratic characters
• On modular forms of half integral weight
• Zeta functions in several variables associated with prehomogeneous vector spaces. I: Functional equations
• Elliptic modular forms arising from zeta functions in two variables attached to the space of binary Hermitian forms
• Zeta functions in several variables associated with prehomogeneous vector spaces. II: A convergence criterion

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