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ON DIRICHLET SERIES CONNECTED WITH MODULAR FORMS OF INTEGRAL AND HALF-INTEGRAL WEIGHT
Mathematics of the USSR-Izvestiya, 1980Convolutions of Dinchlet series connected with modular forms of integral and half-integral weight are investigated. The analytic continuation of such series is constructed, and their values at critical integer points are calculated. Bibliography: 25 titles.
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On the Fourier coefficients of modular forms of half-integral weight
Forum Mathematicum, 2010The author gives a relation between Fourier coefficients of modular forms of half-integral weight and the critical values of quadratic twists of the \(L\)-functions of modular forms of integral weight. In particular, for an indefinite quaternion algebra \(B\) over \(\mathbb{Q}\), he proves an explicit version of a Waldspurger-type formula for the theta
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On Shimura’s Correspondence for Modular Forms of Half-Integral Weight
1981G. Shimura has shown how to attach to each holomorphic cusp form of half-integral weight a modular form of even integral weight. More precisely, suppose f(z) is a cusp form of weight k/2, level N, and character χ.
S. Gelbart, I. Piatetski-Shapiro
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On Fourier coefficients of half-integral weight modular forms
2017In this talk, we give an exposition on some recent work, due to various researchers, on the sign of the Fourier coefficients of modular forms when the Fourier coefficients are real. Our main concern is the case of half-integral weight, and we shall discuss an interesting application due to Ben Kane.
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On multiplier systems and theta functions of half-integral weight for the Hilbert modular group
Journal of Number Theory, 2023Hiroshi Noguchi
exaly
Half-integral weight Eichler integrals and quantum modular forms
Journal of Number Theory, 2016Kathrin Bringmann, Larry Rolen
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Modular Forms with Integral and Half-Integral Weights
2012Xueli Wang, Dingyi Pei
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