On the Fourier coefficients of modular forms of half-integral weight

By Kartik Prasanna. 2009

262 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c52eea9a38bc67eda2f048bc5562b6b8c43bdbd4

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Citations in the corpus

The distribution of closed geodesics on the modular surface, and Duke's theorem (2011, unknown): “is fundamentally different from Linnik’s; it does not rely on ergodic theory but on harmonic analysis of the modular surface SL2(Z)\H, that is on the theory of automorphic forms supplemented by deep arguments from analytic number theory and in particular a breakthrough of Iwaniec [17].”
Sign changes of coefficients of half integral weight modular forms (2007, background): “We suppose that f is contained in the plus space, that is, a(n) = 0 when (−1)kn ≡ 2,3 (mod 4), see [KZ], [ Ko1 ].”
Eichler–Shimura theory for mock modular forms (2013, unknown): “If F ∈ H2−k, then we have that r (ξ2−k(F); z) ≡ − (4π)k−1 Γ(k − 1) · r (Dk−1(F); z) (mod zk−2 − 1).”
Unearthing the visions of a master: harmonic Maass forms and number theory (2008, background): “In the 1980s, Waldspurger [205], and Kohnen and Zagier [135] [136] [137] established that certain half-integral weight modular forms serve as generating functions of a new type.”
Dissipative continuous Euler flows (2012, background): “This problem was raised by Linnik (see [16]), who proved a first result in its direction, and solved thanks to a breakthrough of Iwaniec [14] in the theory of modular forms of half-integral weight (see, for instance, [9] and [19]).”
Effective equidistribution of S-integral points on symmetric varieties (2007, background): “A special case of (A) gives an effective equidistribution for {x ∈ Z3 : f(x) = m} with f = x2 + y2 + z2 or f = x2 + y2 − 3z2, hence giving a different proof of partial cases (because of the restriction onm) of theorems of Iwaniec [33] and Duke [16].”
Faltings heights of CM cycles and derivatives of L-functions (2008, methodology): “On the other hand, by Iwaniec’s bound for the coefficients of half integral weight modular forms as refined by Duke [15, 22], we have b(m1,μ1) ε m1/2−1/28+ε 1 , m1 →∞.”
Twisted L-Functions Over Number Fields and Hilbert’s Eleventh Problem (2009, methodology): “For K = Q, the original breakthrough was achieved by Iwaniec [ I1 ], and the currently strongest bounds are given in [BlH1].”