Advances in mathematics (New York. 1965), ISSN 0001-8708, 2018, Volume 329, pp. 541 - 554

...) as a weight 2 modular form with a pole at z. Although these results rely on the fact that X0...

Divisors of modular forms | Denominator formula | Polar harmonic Maass forms | MATHEMATICS | COEFFICIENTS | MOONSHINE

Divisors of modular forms | Denominator formula | Polar harmonic Maass forms | MATHEMATICS | COEFFICIENTS | MOONSHINE

Journal Article

Mathematische Annalen, ISSN 0025-5831, 3/2013, Volume 355, Issue 3, pp. 1085 - 1121

We use mock modular forms to compute generating functions for the critical values of modular
$$L...

11F03 | Mathematics, general | Mathematics | 11F67 | MATHEMATICS | PERIODS | FOURIER COEFFICIENTS | HALF-INTEGRAL WEIGHT | WEAK MAASS FORMS | AUTOMORPHIC-FORMS | GROUP CO-HOMOLOGY | OPERATORS | L-SERIES | Computer science

11F03 | Mathematics, general | Mathematics | 11F67 | MATHEMATICS | PERIODS | FOURIER COEFFICIENTS | HALF-INTEGRAL WEIGHT | WEAK MAASS FORMS | AUTOMORPHIC-FORMS | GROUP CO-HOMOLOGY | OPERATORS | L-SERIES | Computer science

Journal Article

The Ramanujan journal, ISSN 1382-4090, 11/2016, Volume 41, Issue 1-3, pp. 191 - 232

We discuss the space of polyharmonic Maass forms of even integer weight on PSL (2, Z)\H. We explain the role of the real-analytic Eisenstein series E-k...

Harmonic | Maass forms | Modular forms | Polyharmonic | MATHEMATICS | EISENSTEIN SERIES | LIFTS | MODULAR-FORMS

Harmonic | Maass forms | Modular forms | Polyharmonic | MATHEMATICS | EISENSTEIN SERIES | LIFTS | MODULAR-FORMS

Journal Article

Duke mathematical journal, ISSN 0012-7094, 2015, Volume 164, Issue 1, pp. 39 - 113

The object of this paper is to initiate a study of the Fourier coefficients of a weight 1 harmonic Maass form and relate them to the complex Galois representation associated to a weight 1 newform...

MATHEMATICS | PRODUCTS | S=1 | VALUES | WEIERSTRASS POINTS | HEEGNER POINTS | DERIVATIVES | L-SERIES | MODULAR-FORMS | harmonic modular forms | Galois representations | Maass forms | weight 1 | Stark’s conjectures | 11Sxx | mock-modular | 11Fxx

MATHEMATICS | PRODUCTS | S=1 | VALUES | WEIERSTRASS POINTS | HEEGNER POINTS | DERIVATIVES | L-SERIES | MODULAR-FORMS | harmonic modular forms | Galois representations | Maass forms | weight 1 | Stark’s conjectures | 11Sxx | mock-modular | 11Fxx

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 4/2018, Volume 45, Issue 3, pp. 639 - 645

The ring of Jacobi forms of even weights is generated by the weak Jacobi forms $$\phi _{-2,1}$$
ϕ-2,1
and $$\phi _{0,1}$$
ϕ0,1
. Bringmann and the first author expressed...

Weak Jacobi forms | Maass–Jacobi–Poincaré series | Fourier Analysis | 11F37 | Functions of a Complex Variable | Field Theory and Polynomials | Primary 11F50 | Secondary 11F27 | Mathematics | Number Theory | Combinatorics | Theta decomposition | MATHEMATICS | Maass-Jacobi-Poincare series

Weak Jacobi forms | Maass–Jacobi–Poincaré series | Fourier Analysis | 11F37 | Functions of a Complex Variable | Field Theory and Polynomials | Primary 11F50 | Secondary 11F27 | Mathematics | Number Theory | Combinatorics | Theta decomposition | MATHEMATICS | Maass-Jacobi-Poincare series

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 08/2019, Volume 21, Issue 5, p. 1850029

In this paper, we study generalizations of Poincaré series arising from quadratic forms, which naturally occur as outputs of theta lifts...

polar harmonic Maass forms | CM-values | meromorphic modular forms | regularized Petersson inner products | higher Green’s functions | harmonic Maass forms | weakly holomorphic modular forms | theta lifts | MATHEMATICS, APPLIED | HEIGHTS | MATHEMATICS | ALGEBRAS | higher Green's functions | CYCLES | HALF-INTEGRAL WEIGHT | COEFFICIENTS | AUTOMORPHIC-FORMS | HEEGNER POINTS | DERIVATIVES | Mathematics - Number Theory

polar harmonic Maass forms | CM-values | meromorphic modular forms | regularized Petersson inner products | higher Green’s functions | harmonic Maass forms | weakly holomorphic modular forms | theta lifts | MATHEMATICS, APPLIED | HEIGHTS | MATHEMATICS | ALGEBRAS | higher Green's functions | CYCLES | HALF-INTEGRAL WEIGHT | COEFFICIENTS | AUTOMORPHIC-FORMS | HEEGNER POINTS | DERIVATIVES | Mathematics - Number Theory

Journal Article

Journal of the American Mathematical Society, ISSN 0894-0347, 10/2008, Volume 21, Issue 4, pp. 1085 - 1104

Integers | Series convergence | Mathematical theorems | Integrands | Mathematical transformations | Fourier transformations | Mathematical functions | Mathematical congruence | Combinatorics | Maass forms | Mock theta functions | MATHEMATICS | IDENTITIES | MOCK THETA-FUNCTIONS | CONJECTURES | RAMANUJANS LOST NOTEBOOK

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 07/2018, Volume 332, pp. 403 - 437

...) Maass forms of weight 0 and level 1 and establish a positive-proportional nonvanishing result of such values in the aspect of large spectral parameter in short intervals, which is qualitatively...

Maass forms | Mollifiers | L-functions | Nonvanishing | MATHEMATICS | AUTOMORPHIC L-FUNCTIONS | J(Q) | DIRICHLET L-FUNCTIONS | RANK | ZEROS

Maass forms | Mollifiers | L-functions | Nonvanishing | MATHEMATICS | AUTOMORPHIC L-FUNCTIONS | J(Q) | DIRICHLET L-FUNCTIONS | RANK | ZEROS

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 03/2014, Volume 411, Issue 1, pp. 429 - 441

Recently, K. Bringmann, P. Guerzhoy, Z. Kent and K. Ono studied the connection between Eichler integrals and the holomorphic parts of harmonic weak Maass forms on the full modular group...

Harmonic weak Maass form | Period function | Eichler integral | Period polynomial | MATHEMATICS | MATHEMATICS, APPLIED | COHOMOLOGY | THEOREM | Mathematics - Number Theory

Harmonic weak Maass form | Period function | Eichler integral | Period polynomial | MATHEMATICS | MATHEMATICS, APPLIED | COHOMOLOGY | THEOREM | Mathematics - Number Theory

Journal Article

Journal of number theory, ISSN 0022-314X, 03/2015, Volume 148, pp. 272 - 287

Suppose π1 and π2 are two Hecke–Maass cusp forms for SL(3,Z) such that for all primitive characters χ we haveL(12,π1⊗χ)=L(12,π2⊗χ). Then we show that π1=π2.

[formula omitted] Hecke Maass form | Twisted central L-values | GL Hecke Maass form | MATHEMATICS | MODULAR-FORMS

[formula omitted] Hecke Maass form | Twisted central L-values | GL Hecke Maass form | MATHEMATICS | MODULAR-FORMS

Journal Article

Memoirs of the American Mathematical Society, ISSN 0065-9266, 2015, Volume 237, Issue 1118

We construct explicit isomorphisms between spaces of Maass forms and mixed parabolic cohomology groups.

cohomology group | principal series | Maass form | parabolic cohomology | period function | Petersson scalar product | Cup product | Parabolic cohomology | Period function | Cohomology group | Principal series

cohomology group | principal series | Maass form | parabolic cohomology | period function | Petersson scalar product | Cup product | Parabolic cohomology | Period function | Cohomology group | Principal series

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 2017, Volume 145, Issue 10, pp. 4161 - 4174

The Maass form twisted Shintani L-functions are introduced, and some of their analytic properties are studied...

Equidistribution | Shintani zeta function | Maass form | MATHEMATICS | MATHEMATICS, APPLIED | COEFFICIENTS | 4TH

Equidistribution | Shintani zeta function | Maass form | MATHEMATICS | MATHEMATICS, APPLIED | COEFFICIENTS | 4TH

Journal Article

American journal of mathematics, ISSN 0002-9327, 12/2014, Volume 136, Issue 6, pp. 1693 - 1745

We consider the problem of classifying all positive-definite integer-valued quadratic forms that represent all positive odd integers...

Integers | Discriminants | Numbers | Inner products | Mathematical lattices | Coefficients | Fourier coefficients | Odd numbers | Escalators | Conceptual lattices | Forms, Quadratic | Number theory | Signed numbers | MATHEMATICS | FUNCTIONAL-EQUATIONS | FOURIER COEFFICIENTS | BOUNDS | LINE | HALF-INTEGRAL WEIGHT | MAASS FORMS | L-SERIES | MODULAR-FORMS | LOCAL-DENSITIES | Numbers, Natural | Analysis | Mathematical problems | Theorems | Linear equations | Quadratic programming

Integers | Discriminants | Numbers | Inner products | Mathematical lattices | Coefficients | Fourier coefficients | Odd numbers | Escalators | Conceptual lattices | Forms, Quadratic | Number theory | Signed numbers | MATHEMATICS | FUNCTIONAL-EQUATIONS | FOURIER COEFFICIENTS | BOUNDS | LINE | HALF-INTEGRAL WEIGHT | MAASS FORMS | L-SERIES | MODULAR-FORMS | LOCAL-DENSITIES | Numbers, Natural | Analysis | Mathematical problems | Theorems | Linear equations | Quadratic programming

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 10/2018, Volume 47, Issue 1, pp. 185 - 200

Extending the approach of Iwaniec and Duke, we present strong uniform bounds for Fourier coefficients of half-integral weight cusp forms of level N...

Primary 11F03 | Waring’s problem | Functions of a Complex Variable | Field Theory and Polynomials | Mathematics | 11F30 | Maaß forms | Fourier Analysis | Ternary quadratic forms | Number Theory | Combinatorics | Half-integral weight cusp forms | 11P05 | THETA-SERIES | MATHEMATICS | Waring's problem | BOUNDS | Maa ss forms | QUADRATIC-FORMS | MODULAR-FORMS

Primary 11F03 | Waring’s problem | Functions of a Complex Variable | Field Theory and Polynomials | Mathematics | 11F30 | Maaß forms | Fourier Analysis | Ternary quadratic forms | Number Theory | Combinatorics | Half-integral weight cusp forms | 11P05 | THETA-SERIES | MATHEMATICS | Waring's problem | BOUNDS | Maa ss forms | QUADRATIC-FORMS | MODULAR-FORMS

Journal Article

Journal of number theory, ISSN 0022-314X, 04/2017, Volume 173, pp. 1 - 22

Let f be a primitive Maass cusp form for a congruence subgroup Γ
(D)⊂SL(2,Z) and λ
(n) its n-th Fourier coefficient...

Laplace eigenvalue | Maass forms for congruence subgroups | Resonance | Voronoi summation formula | MATHEMATICS | SUMS | Analysis | Algorithms | Mathematics - Number Theory

Laplace eigenvalue | Maass forms for congruence subgroups | Resonance | Voronoi summation formula | MATHEMATICS | SUMS | Analysis | Algorithms | Mathematics - Number Theory

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 6/2013, Volume 31, Issue 1, pp. 147 - 161

In this paper, we consider the space of second order cusp forms. We determine that this space is precisely the same as a certain subspace of mixed mock modular forms. Based upon Poincaré...

Harmonic Maass forms | Modular forms | 11F37 | Functions of a Complex Variable | Field Theory and Polynomials | Mathematics | 11F12 | 11F11 | Fourier Analysis | Poincaré series | Mixed mock modular forms | Number Theory | Combinatorics | Second-order modular forms | SERIES | RANKS | THETA-FUNCTIONS | POSITIVE DIMENSION | MAASS FORMS | Poincare series | MATHEMATICS | COEFFICIENTS | SUPERALGEBRAS | PARTITIONS

Harmonic Maass forms | Modular forms | 11F37 | Functions of a Complex Variable | Field Theory and Polynomials | Mathematics | 11F12 | 11F11 | Fourier Analysis | Poincaré series | Mixed mock modular forms | Number Theory | Combinatorics | Second-order modular forms | SERIES | RANKS | THETA-FUNCTIONS | POSITIVE DIMENSION | MAASS FORMS | Poincare series | MATHEMATICS | COEFFICIENTS | SUPERALGEBRAS | PARTITIONS

Journal Article

17.
Full Text
A note on the characterizations of Jacobi cusp forms and cusp forms of Maass Spezialschar

The Ramanujan Journal, ISSN 1382-4090, 8/2015, Volume 37, Issue 3, pp. 535 - 539

In this paper, we give characterizations of Jacobi cusp forms of weight
$$k$$
k
and index
$$1$$
1
on a congruence subgroup...

Maass Spezialschar | 11F46 | Fourier Analysis | Functions of a Complex Variable | Field Theory and Polynomials | 11F50 | Mathematics | 11F30 | Number Theory | Jacobi forms | Combinatorics | Fourier coefficients of automorphic forms | MATHEMATICS | DEGREE-2 | MODULAR-FORMS

Maass Spezialschar | 11F46 | Fourier Analysis | Functions of a Complex Variable | Field Theory and Polynomials | 11F50 | Mathematics | 11F30 | Number Theory | Jacobi forms | Combinatorics | Fourier coefficients of automorphic forms | MATHEMATICS | DEGREE-2 | MODULAR-FORMS

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 1/2014, Volume 33, Issue 1, pp. 55 - 82

It is shown that each complex conjugate of a meromorphic modular form for
$\mathrm{SL}_{2}(\mathbb{Z})$
of any complex weight p occurs as the image of a harmonic modular form under the operator...

Fourier Analysis | 11F37 | Functions of a Complex Variable | Field Theory and Polynomials | 11F72 | Harmonic lift | Mathematics | Number Theory | Combinatorics | Modular form | MATHEMATICS | MAASS FORMS

Fourier Analysis | 11F37 | Functions of a Complex Variable | Field Theory and Polynomials | 11F72 | Harmonic lift | Mathematics | Number Theory | Combinatorics | Modular form | MATHEMATICS | MAASS FORMS

Journal Article

Proceedings of the National Academy of Sciences - PNAS, ISSN 0027-8424, 4/2010, Volume 107, Issue 14, pp. 6169 - 6174

A "mock modular form" is the holomorphic part of a harmonic Maass form f. The nonholomorphic part of f is a period integral of its "shadow," a cusp form g...

Integers | Mathematical theorems | Algebra | Differential operators | Mathematical functions | Coefficients | Fourier coefficients | Mathematical cusps | College mathematics | Mock theta function | Harmonic Maass form | harmonic Maass form | mock theta function | MAASS FORMS | MULTIDISCIPLINARY SCIENCES | Transformations (Mathematics) | Research | Geometry, Algebraic | Physical Sciences

Integers | Mathematical theorems | Algebra | Differential operators | Mathematical functions | Coefficients | Fourier coefficients | Mathematical cusps | College mathematics | Mock theta function | Harmonic Maass form | harmonic Maass form | mock theta function | MAASS FORMS | MULTIDISCIPLINARY SCIENCES | Transformations (Mathematics) | Research | Geometry, Algebraic | Physical Sciences

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2017, Volume 19, Issue 11, pp. 3549 - 3573

Let $f$ be an $L^2$-normalized Hecke–Maass cuspidal newform of level $N$ and Laplace eigenvalue $\lambda$. It is shown that $\|f\|_\infty \ll_{\lambda,...

General | Number theory | Amplification | Fourier Coefficients | Maass Form | Sup-Norm | MATHEMATICS | amplification | MATHEMATICS, APPLIED | Maass form | BOUNDS | sup-norm | EIGENFUNCTIONS | Fourier coefficients

General | Number theory | Amplification | Fourier Coefficients | Maass Form | Sup-Norm | MATHEMATICS | amplification | MATHEMATICS, APPLIED | Maass form | BOUNDS | sup-norm | EIGENFUNCTIONS | Fourier coefficients

Journal Article

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