A converse theorem for second-order modular forms of level N

Imamoḡlu, Özlem; Martin, Yves

doi:10.4064/aa123-4-5

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Cited by 6 publications

(7 citation statements)

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“…As an approach to the abcconjecture, Dorian Goldfeld introduced Eisenstein-series twisted by modular symbols [CDO02, GG00,Gol02], which are higher order forms. Finally, spaces of higher order forms are natural receptacles of converse theorems [Far02,IM06].…”

Section: Introductionmentioning

confidence: 99%

Invariants, cohomology, and automorphic forms of higher order

Deitmar

2012

Sel. Math. New Ser.

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A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains the fact that L-functions of higher order forms have no Euler-product. Higher order cohomology is introduced, classical results of Borel are generalized and a higher order version of Borel's conjecture is stated.

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Section: Introductionmentioning

confidence: 99%

Invariants, cohomology, and automorphic forms of higher order

Deitmar

2012

Sel. Math. New Ser.

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“…Higher order modular forms show up in various contexts, for instance in percolation theory [16], or in the theory of Eisenstein-series twisted by modular symbols [2,12,13]. Finally, spaces of higher order forms are natural receptacles of converse theorems [10,15].…”

Section: Introductionmentioning

confidence: 99%

Higher order invariants in the case of compact quotients

Deitmar

2010

Open Mathematics

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“…L-functions of second order forms have been studied in [4,10], Poincaré series attached to higher order forms have been investigated in [11], dimensions of spaces of second order forms have been determined in [5].…”

Section: Introductionmentioning

confidence: 99%