WebOct 1, 2024 · A Hilbert modular formof (parallel) weight k∈N0is a holomorphic function of two variables f:H×H→Cwhich satisfiesf(aτ1+bcτ1+d,a′τ2+b′c′τ2+d′)=(cτ1+d)k(c′τ2+d′)kf(τ1,τ2)for all M=(abcd)∈ΓK=SL2(OK). Here a′denotes the conjugate of a∈K. In mathematics, a Hilbert modular form is a generalization of modular forms to functions of two or more variables. It is a (complex) analytic function on the m-fold product of upper half-planes $${\displaystyle {\mathcal {H}}}$$ satisfying a certain kind of functional equation. See more These modular forms, for real quadratic fields, were first treated in the 1901 Göttingen University Habilitationssschrift of Otto Blumenthal. There he mentions that David Hilbert had considered them initially in work from 1893-4, … See more • Siegel modular form • Hilbert modular surface See more
Hecke operators and Hilbert modular forms - UNCG
WebThe Hilbert modular group Γ K= SL 2(O K) acts on H × H as follows. If (z 1,z 2) ∈ H×H and M= a b c d ∈ Γ Kthen M·(z 1,z 2) = az 1+b cz 1+d , az 2+b cz 2+d . A Hilbert modular form of weight kis, roughly speaking, a meromorphic function Ψ(z 1,z 2) on H×H such that Ψ(M·(z 1,z 2)) = (cz 1+d)k(cz 2+d)kΨ(z 1,z 2). WebHilbert modular surfaces CurtisT.McMullen 31March,2002 Abstract This paper exhibits an infinite collection of algebraic curves iso-metrically embedded in the moduli space of Riemann surfaces of genus two. These Teichmu¨ller curves lie on Hilbert modular surfaces param- ... form for the given action of K is simply the intersection P ... northeast generals na3hl game result
Hilbert modular forms and p -adic Hodge theory - Cambridge Core
WebModular Homes of North Carolina (MHNC) is a builder of fine homes ranging in sizes from 700 square feet to in excess of 6000 square feet. MHNC builds just about every style of … WebApr 16, 2024 · The main result of this paper shows the first connection between the Kronecker series and the critical L -values of Hilbert modular forms over the totally real number fields. It also gives a systematic way to compute Hilbert Hecke eigenforms and the special values of L -functions by taking the expansions of the Kronecker series. WebJan 3, 2024 · modular forms. REMARK.In [26], Liu uses Hirzebruch–Zagier cycles to construct a collection of global cohomology classes for the self-dual twist of M Lv.F/ M L v.g/, where F is a Hilbert modular form of parallel weight 2 and g is an elliptic modular form of weight 2. These cohomology classes stand in the same relation to the how to retrieve wifi password windows 11