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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
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 $$L... 
11F03 | Mathematics, general | Mathematics | 11F67 | MATHEMATICS | PERIODS | FOURIER COEFFICIENTS | HALF-INTEGRAL WEIGHT | WEAK MAASS FORMS | AUTOMORPHIC-FORMS | GROUP CO-HOMOLOGY | OPERATORS | L-SERIES | Computer science
Journal Article
The Ramanujan journal, ISSN 1382-4090, 11/2016, Volume 41, Issue 1-3, pp. 191 - 232
We discuss the space of polyharmonic Maass forms of even integer weight on PSL (2, Z)\H. We explain the role of the real-analytic Eisenstein series E-k... 
Harmonic | Maass forms | Modular forms | Polyharmonic | MATHEMATICS | EISENSTEIN SERIES | LIFTS | MODULAR-FORMS
Journal Article
by Duke, W and Li, Y
Duke mathematical journal, ISSN 0012-7094, 2015, Volume 164, Issue 1, pp. 39 - 113
The object of this paper is to initiate a study of the Fourier coefficients of a weight 1 harmonic Maass form and relate them to the complex Galois representation associated to a weight 1 newform... 
MATHEMATICS | PRODUCTS | S=1 | VALUES | WEIERSTRASS POINTS | HEEGNER POINTS | DERIVATIVES | L-SERIES | MODULAR-FORMS | harmonic modular forms | Galois representations | Maass forms | weight 1 | Stark’s conjectures | 11Sxx | mock-modular | 11Fxx
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 4/2018, Volume 45, Issue 3, pp. 639 - 645
The ring of Jacobi forms of even weights is generated by the weak Jacobi forms $$\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
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 08/2019, Volume 21, Issue 5, p. 1850029
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
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
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
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
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
Journal Article
American journal of mathematics, ISSN 0002-9327, 12/2014, Volume 136, Issue 6, pp. 1693 - 1745
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
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
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
Journal Article
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
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
Journal Article
Proceedings of the National Academy of Sciences - PNAS, ISSN 0027-8424, 4/2010, Volume 107, Issue 14, pp. 6169 - 6174
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
Journal Article
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