On congruence modules related to Hilbert Eisenstein series
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DOI: 10.1007/s00209-020-02486-9
Abstract: We generalize the work of Ohta on the congruence modules attached to elliptic Eisenstein series to the setting of Hilbert modular forms. Our work involves three parts. In the first part, we construct Eisenstein series… read more here.
Keywords: modules related; eisenstein series; congruence modules; series ... See more keywords
Orthogonal Eisenstein series at harmonic points and modular forms of singular weight
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DOI: 10.1007/s00209-022-03011-w
Abstract: We investigate the behaviour of orthogonal non-holomorphic Eisenstein series at their harmonic points by using theta lifts. In the case of singular weight, we show that the orthogonal non-holomorphic Eisenstein series that can be written… read more here.
Keywords: modular forms; eisenstein series; series; series harmonic ... See more keywords
The finiteness of derivation-invariant prime ideals and the algebraic independence of the Eisenstein series
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DOI: 10.1007/s11139-021-00404-z
Abstract: We prove that for a graded algebra $$\mathcal {A}$$ with a derivation $$D_{\mathcal {A}}$$ satisfying certain conditions, and a bi-graded algebra $$\mathcal {A}[q]$$ with an extended derivation D of $$D_{\mathcal {A}}$$ , there are only… read more here.
Keywords: algebraic independence; derivation; eisenstein series; prime ideals ... See more keywords
On Eisenstein series in M2(Γ0(N)) and their applications
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DOI: 10.1016/j.jnt.2018.06.010
Abstract: Abstract Let k , N ∈ N with N square-free and k > 1 . We prove an orthogonal relation and use this to compute the Fourier coefficients of the Eisenstein part of any f… read more here.
Keywords: series applications; eisenstein series;
Explicit calculations with Eisenstein series
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DOI: 10.1016/j.jnt.2018.11.007
Abstract: We find explicit change-of-basis formulas between Eisenstein series attached to cusps, and newform Eisenstein series attached to pairs of primitive Dirichlet characters. As a consequence, we prove a Bruggeman-Kuznetsov formula for newforms of square-free level… read more here.
Keywords: eisenstein series; explicit calculations; series; calculations eisenstein ... See more keywords
Monomials of Eisenstein series
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DOI: 10.1016/j.jnt.2020.09.002
Abstract: Abstract Let E k ( z ) be the normalized Eisenstein series of weight k for the modular group SL ( 2 , Z ) . We study the zeros of E k to prove… read more here.
Keywords: series; eisenstein series; monomials eisenstein;
Dirichlet series of two variables, real analytic Jacobi–Eisenstein series of matrix index, and Katok–Sarnak type result
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DOI: 10.1515/forum-2017-0119
Abstract: We study a real analytic Jacobi–Eisenstein series of matrix index and deduce several arithmetically interesting properties. In particular, we prove the followings: (a) Its Fourier coefficients are proportional to the average values of the Eisenstein… read more here.
Keywords: analytic jacobi; jacobi eisenstein; eisenstein series; real analytic ... See more keywords