Results 91 to 100 of about 230 (149)
L-series for Vector-Valued Weakly Holomorphic Modular Forms and Converse Theorems
Canadian Journal of MathematicsAbstract We introduce the L-series of weakly holomorphic modular forms using Laplace transforms and give their functional equations. We then determine converse theorems for vector-valued harmonic weak Maass forms, Jacobi forms, and elliptic modular forms of half-integral weight in Kohnen plus space.
Lim, Subong, Raji, Wissam
openaire +2 more sources
Modular forms, partitions, and q-series
, 2020 This dissertation explores results pertaining to partition theory and its q-series identities using techniques from modular forms. In particular, Chapter 2 proves congruences for k-colored generalized Frobenius partitions originally dened by George ...
Wieczorek, Margaret Anne
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4-manifolds and topological modular forms [PDF]
, 2018 We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1,0) theories on 4-manifolds with flavor symmetry backgrounds.
Gukov, Sergei +3 more
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Differential operators on polar harmonic Maass forms and elliptic duality
, 2019 In this paper, we study polar harmonic Maass forms of negative integral weight. Using work of Fay, we construct Poincaré series which span the space of such forms and show that their elliptic coefficients exhibit duality properties which are similar to ...
Jenkins, P +5 more
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Traces of singular moduli on Hilbert modular surfaces
, 2005 Suppose that p ≡ 1 (mod 4) is a prime, and that OK is the ring of integers of K: = Q(√p). A classical result of Hirzebruch and Zagier asserts that certain generating functions for the intersection numbers of Hirzebruch-Zagier divisors on the Hilbert ...
Rouse, Jeremy +5 more
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Weakly Holomorphic Modular Forms in Prime Power Levels of Genus Zero
, 2016 Let N ∈ {8,9,16,25} and let M#0(N) be the space of level N weakly holomorphic modular functions with poles only at the cusp at infinity. We explicitly construct a canonical basis for M#0(N) indexed by the order of the pole at infinity and show that many ...
Thornton, David Joshua
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ZAGIER DUALITY FOR HARMONIC WEAK MAASS FORMS OF INTEGRAL WEIGHT
, 2019 We show the existence of "Zagier duality" between vector valued harmonic weak Maass forms and vector valued weakly holomorphic modular forms of integral weight.
Cho, B, Choie, Y
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Nonholomorphic Ramanujan-type congruences for Hurwitz class numbers. [PDF]
Proc Natl Acad Sci U S A, 2020 Beckwith O, Raum M, Richter OK.
europepmc +1 more source
The Arithmetic of Modular Grids
, 2018 Let Mk(∞) (Gamma, nu) denote the space of weight k weakly holomorphic weight modular forms with poles only at the cusp (∞), and let widehat Mk(∞) (Gamma, nu) subseteq Mk(∞) (Gamma, nu) denote the space of weight k weakly holomorphic modular forms in Mk(∞)
Molnar, Grant Steven
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Ramanujan's influence on string theory, black holes and moonshine. [PDF]
Philos Trans A Math Phys Eng Sci, 2020 Harvey JA.
europepmc +1 more source