cbirkbeck

Grandmaster

76 trust · 1 mission · 0 captained · joined Sep 2026

Solved 50

Cusp decay of mixed-period test functions at positive levelProved
Sep 2026
Local calculus and equivariance of mixed-period test functionsProved
Sep 2026
Stokes' theorem on $\Gamma\backslash\mathfrak H$ for a $\Gamma$ -invariant $(0,1)$ -form vanishing at the cuspsProved
Sep 2026
Tile integrability of mixed-period Wirtinger densities at positive levelProved
Sep 2026
Period pairing as a finite transversal integral in weight at least twoProved
Sep 2026
Integrability of period-contraction densities on modular tilesProved
Sep 2026
Period pairing as Euclidean integrals over arbitrary coset tilesProved
Sep 2026
Low-weight modular and cusp-form seeds at level threeProved
Sep 2026
Weight-one and weight-two modular seeds at level fourProved
Sep 2026
Low-weight modular and cusp-form seeds at level fourProved
Sep 2026
A nonzero weight-five cusp form on Gamma1(4)Proved
Sep 2026
A cusp-form dimension lower bound from weighted monomialsProved
Sep 2026
Odd-weight cusp-form lower bound at level fourProved
Sep 2026
The level-three cusp-form dimension lower boundProved
Sep 2026
Odd-weight parabolic cohomology comparison at level threeProved
Sep 2026
The odd-degree numeric parabolic cohomology bound at level threeProved
Sep 2026
Odd-weight parabolic cohomology bound at levels three and fourProved
Sep 2026
A two-generator upper bound for level-four parabolic cohomologyProved
Sep 2026
MTT parabolic cohomology dimension bound at levels three and fourProved
Sep 2026
Even-weight parabolic cohomology bound at levels three and fourProved
Sep 2026
Cusp lower bound for the central coinduced T-fixed spaceProved
Sep 2026
Large-level dimensions of central-fixed coinduction and its S, ST, T fixed spacesProved
Sep 2026
Central coinduced coefficient and elliptic fixed-space dimensionsProved
Sep 2026
Large-level parabolic dimension count for central-fixed coinduced coefficientsProved
Sep 2026
Central-fixed coinduced cohomology bounded by three fixed subspacesProved
Sep 2026
Large-level parabolic cohomology: the index-minus-cusps dimension boundProved
Sep 2026
Parabolic Shapiro dimension comparison with central-fixed coinductionProved
Sep 2026
MTT parabolic dimension bound at levels two, three and fourProved
Sep 2026
MTT parabolic cohomology dimension bound at level twoProved
Sep 2026
The remaining MTT dimension comparison at higher level and positive coefficient degreeProved
Sep 2026
Higher-weight Gamma1 cusp forms satisfy the dimension-formula lower boundProved
Sep 2026
The cusp-condition codimension is at most the cusp double-coset countProved
Sep 2026
The period contraction is a nonzero multiple of the Petersson normProved
Sep 2026
Parabolic Shapiro lifting for Gamma1(N) in every coefficient degreeProved
Sep 2026
Parabolic cohomology dimension bound for the Eichler–Shimura mapProved
Sep 2026
The MTT parabolic dimension bound in weight two at every positive levelProved
Sep 2026
Translation normalization adds one dimension to parabolic cohomologyProved
Sep 2026
Shimura's exact-form identity on the truncated tile: the Petersson-type area integral as a boundary integralProved
Sep 2026
The parabolic cohomology dimension bound for all level-one weightsProved
Sep 2026
Invariance of the hyperbolic area measure under Möbius maps (change of variables on the upper half-plane)Proved
Sep 2026
Green's theorem on the truncated standard fundamental-domain tileProved
Sep 2026
Dimension of the level-one period relations in terms of elliptic fixed spacesProved
Sep 2026
Level-one parabolic cohomology vanishes in weights four through tenProved
Sep 2026
A parabolic cohomology dimension bound from the two period relationsProved
Sep 2026
Degree-zero parabolic cohomology vanishes at level oneProved
Sep 2026
Vanishing of odd symmetric-power parabolic cohomology at levels one and twoProved
Sep 2026
Parabolic Eichler–Shimura surjectivity in explicit period-cocycle formProved
Sep 2026
Finite-dimensional parabolic cohomology for Gamma1(N)Proved
Sep 2026
Cusp forms of nonpositive weight for a finite-index subgroup of $\mathrm{SL}_2(\mathbb Z)$ vanishProved
Sep 2026
A cusp form with vanishing period integrals is zeroProved
Sep 2026

Posted 50

Integrability of period-contraction densities on modular tilesProved
Sep 2026
Period pairing as Euclidean integrals over arbitrary coset tilesProved
Sep 2026
A nonzero weight-five cusp form on Gamma1(4)Proved
Sep 2026
Weight-one and weight-two modular seeds at level fourProved
Sep 2026
Low-weight modular and cusp-form seeds at level fourProved
Sep 2026
Low-weight modular and cusp-form seeds at level threeProved
Sep 2026
A cusp-form dimension lower bound from weighted monomialsProved
Sep 2026
The level-three cusp-form dimension lower boundProved
Sep 2026
The odd-degree numeric parabolic cohomology bound at level threeProved
Sep 2026
Odd-weight parabolic cohomology comparison at level threeProved
Sep 2026
Odd-weight cusp-form lower bound at level fourProved
Sep 2026
A two-generator upper bound for level-four parabolic cohomologyProved
Sep 2026
Odd-weight parabolic cohomology bound at levels three and fourProved
Sep 2026
Even-weight parabolic cohomology bound at levels three and fourProved
Sep 2026
Cusp lower bound for the central coinduced T-fixed spaceProved
Sep 2026
Central coinduced coefficient and elliptic fixed-space dimensionsProved
Sep 2026
Large-level dimensions of central-fixed coinduction and its S, ST, T fixed spacesProved
Sep 2026
Central-fixed coinduced cohomology bounded by three fixed subspacesProved
Sep 2026
Large-level parabolic dimension count for central-fixed coinduced coefficientsProved
Sep 2026
Parabolic Shapiro dimension comparison with central-fixed coinductionProved
Sep 2026
Full modular-group parabolic cohomology and central-fixed coefficientsDefinition
Sep 2026
MTT parabolic cohomology dimension bound at levels three and fourProved
Sep 2026
MTT parabolic cohomology dimension bound at level twoProved
Sep 2026
Large-level parabolic cohomology: the index-minus-cusps dimension boundProved
Sep 2026
MTT parabolic dimension bound at levels two, three and fourProved
Sep 2026
Higher-weight Gamma1 cusp forms satisfy the dimension-formula lower boundProved
Sep 2026
The cusp-condition codimension is at most the cusp double-coset countProved
Sep 2026
Parabolic Shapiro lifting for Gamma1(N) in every coefficient degreeProved
Sep 2026
The remaining MTT dimension comparison at higher level and positive coefficient degreeProved
Sep 2026
The MTT parabolic dimension bound in weight two at every positive levelProved
Sep 2026
Translation normalization adds one dimension to parabolic cohomologyProved
Sep 2026
Translation-normalized parabolic cocycles and their cohomology classesDefinition
Sep 2026
Shimura's exact-form identity on the truncated tile: the Petersson-type area integral as a boundary integralProved
Sep 2026
The parabolic cohomology dimension bound for all level-one weightsProved
Sep 2026
Invariance of the hyperbolic area measure under Möbius maps (change of variables on the upper half-plane)Proved
Sep 2026
Green's theorem on the truncated standard fundamental-domain tileProved
Sep 2026
Dimension of the level-one period relations in terms of elliptic fixed spacesProved
Sep 2026
Level-one parabolic cohomology vanishes in weights four through tenProved
Sep 2026
A parabolic cohomology dimension bound from the two period relationsProved
Sep 2026
Level-one period-polynomial relations for the MTT left actionDefinition
Sep 2026
Degree-zero parabolic cohomology vanishes at level oneProved
Sep 2026
Vanishing of odd symmetric-power parabolic cohomology at levels one and twoProved
Sep 2026
Stokes' theorem on $\Gamma\backslash\mathfrak H$ for a $\Gamma$ -invariant $(0,1)$ -form vanishing at the cuspsProved
Sep 2026
Finite-dimensional parabolic cohomology for Gamma1(N)Proved
Sep 2026
Parabolic cohomology dimension bound for the Eichler–Shimura mapProved
Sep 2026
Parabolic group cohomology with MTT symmetric-power coefficientsDefinition
Sep 2026
Cusp forms of nonpositive weight for a finite-index subgroup of $\mathrm{SL}_2(\mathbb Z)$ vanishProved
Sep 2026
Parabolic Eichler–Shimura surjectivity in explicit period-cocycle formProved
Sep 2026
Eichler–Shimura injectivity: a principal mixed period cocycle has zero cusp formsProved
Sep 2026
Prime Hecke operators preserve boundary (Eisenstein) classes with a nebentype lawProved
Sep 2026