Concentration of closed geodesics in the homology of modular curves
Forum of Mathematics, Sigma, 2023 We prove that the homology classes of closed geodesics associated to subgroups of narrow class groups of real quadratic fields concentrate around the Eisenstein line.
Asbjørn Christian Nordentoft
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Error term of the mean value theorem for binary Egyptian fractions
Open Mathematics, 2020 In this article, the error term of the mean value theorem for binary Egyptian fractions is studied. An error term of prime number theorem type is obtained unconditionally. Under Riemann hypothesis, a power saving can be obtained.
Xiao Xuanxuan, Zhai Wenguang
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PERIOD IDENTITIES OF CM FORMS ON QUATERNION ALGEBRAS
Forum of Mathematics, Sigma, 2020 Waldspurger’s formula gives an identity between the norm of a torus period and an $L$-function of the twist of an automorphic representation on GL(2).
CHARLOTTE CHAN
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Explicit construction of mock modular forms from weakly holomorphic Hecke eigenforms
Open Mathematics, 2022 Extending our previous work we construct weakly holomorphic Hecke eigenforms whose period polynomials correspond to elements in a basis consisting of odd and even Hecke eigenpolynomials induced by only cusp forms.
Choi SoYoung, Kim Chang Heon
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A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS
Forum of Mathematics, Sigma, 2020 We introduce a new family of real-analytic modular forms on the upper-half plane. They are arguably the simplest class of ‘mixed’ versions of modular forms of level one and are constructed out of real and imaginary parts of iterated integrals of ...
FRANCIS BROWN
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P‐adic L‐functions of Bianchi modular forms
Proceedings of the London Mathematical Society, Volume 114, Issue 4, Page 614-656, April 2017., 2017 Abstract The theory of overconvergent modular symbols, developed by Rob Pollack and Glenn Stevens, gives a beautiful and effective construction of the p‐adic L‐function of a modular form. In this paper, we give an analogue of their results for Bianchi modular forms, that is, modular forms over imaginary quadratic fields. In particular, we prove control
Chris Williams
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Shintani and Shimura lifts of cusp forms on certain arithmetic groups and their applications
Open Mathematics, 2017 For an odd and squarefree level N, Kohnen proved that there is a canonically defined subspace Sκ+12new(N)⊂Sκ+12(N),andSκ+12new(N)andS2knew(N)$S_{\kappa+\frac{1}{2}}^{\mathrm{n}\mathrm{e}\mathrm{w}}(N)\subset S_{\kappa+\frac{1}{2}}(N),\,\,{\text{and ...
Choi SoYoung, Kim Chang Heon
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ANDRÉ–OORT CONJECTURE AND NONVANISHING OF CENTRAL $L$ -VALUES OVER HILBERT CLASS FIELDS
Forum of Mathematics, Sigma, 2016 Let $F/\mathbf{Q}$ be a totally real field and $K/F$ a ...
ASHAY A. BURUNGALE, HARUZO HIDA
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On the algebraicity of coefficients of half-integral weight mock modular forms
Open Mathematics, 2018 Extending works of Ono and Boylan to the half-integral weight case, we relate the algebraicity of Fourier coefficients of half-integral weight mock modular forms to the vanishing of Fourier coefficients of their shadows.
Choi SoYoung, Kim Chang Heon
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ZETA ELEMENTS IN DEPTH 3 AND THE FUNDAMENTAL LIE ALGEBRA OF THE INFINITESIMAL TATE CURVE
Forum of Mathematics, Sigma, 2017 This paper draws connections between the double shuffle equations and structure of associators; Hain and Matsumoto’s universal mixed elliptic motives; and the Rankin–Selberg method for modular forms for
FRANCIS BROWN
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