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The shifted fourth moment of modular form L -functions in the weight aspect
Canadian Journal of Mathematics - Journal Canadien de MathematiquesWe prove a reciprocity type formula for the fourth moment of L-functions associated to holomorphic primitive cusp forms of level one and large weight which relates it to the eighth moment of the Riemann zeta function and the dual weighted fourth moments ...
O. Balkanova, D. Frolenkov
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Modular Construction Of P -Adic L -Functions For Real Quadratic Fields
International Journal of Number TheoryThis paper provides a modular construction of p-adic L-functions for real quadratic fields. The key ingredient in this construction is the use of period integrals of automorphic forms. This work extends the previous results of Darmon and Dasgupta.
Pin-Chi Hung, Zhi-Lin Zhang
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Automorphisms of the Modular Function Field
1987If N, M are positive integers, and N|M, then we have a canonical homomorphism $$G{L_2}\left( {Z/MZ} \right)\,\, \to \,\,G{L_2}\left( {Z/NZ} \right),$$ and we can take the projective limit.
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Machine learning automorphic forms for black holes
arXiv.orgModular, Jacobi, and mock-modular forms serve as generating functions for BPS black hole degeneracies. By training feed-forward neural networks on Fourier coefficients of automorphic forms derived from the Dedekind eta function, Eisenstein series, and ...
Vishnu Jejjala +4 more
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On discrete mean value of automorphic L-functions $$^{*}$$ ∗
Indian journal of pure and applied mathematics, 2023Yu Chen, Weili Yao
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Mean-square estimate of automorphic L-functions
Frontiers of Mathematics in China, 2020Weili Yao
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The Annals of Mathematics, 1981
As to the meaning of the symbols, the reader is referred to the introduction of Part I. We recall here only that F is a totally real algebraic number field of degree n, and w denotes the Fourier coefficients of an elliptic modular form 52(z) = E wQ(a)e2q'iaz.
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As to the meaning of the symbols, the reader is referred to the introduction of Part I. We recall here only that F is a totally real algebraic number field of degree n, and w denotes the Fourier coefficients of an elliptic modular form 52(z) = E wQ(a)e2q'iaz.
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One-line formula for automorphic differential operators on Siegel modular forms
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 2019T. Ibukiyama
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Upper bounds for the moments of automorphic L-functions for GL(2)
Lithuanian Mathematical JournalMinghua Chen, Hengcai Tang
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