Results 1 to 10 of about 15 (15)

Central L‐values of elliptic curves and local polynomials

Proceedings of the London Mathematical Society, Volume 120, Issue 5, Page 742-769, May 2020., 2020
Abstract Here we study the recently introduced notion of a locally harmonic Maass form and its applications to the theory of L‐functions. In particular, we find a criterion for vanishing of certain twisted central L‐values of a family of elliptic curves, whereby vanishing occurs precisely when the values of two finite sums over canonical binary ...
Stephan Ehlen, Pavel Guerzhoy, Ben Kane, Larry Rolen   +3 more
wiley   +1 more source

Bounds for twisted symmetric square L-functions via half-integral weight periods

Forum of Mathematics, Sigma, 2020
We establish the first moment bound $$\begin{align*}\sum_{\varphi} L(\varphi \otimes \varphi \otimes \Psi, \tfrac{1}{2}) \ll_\varepsilon p^{5/4+\varepsilon} \end{align*}$$ for triple product L-functions, where $\Psi $ is a fixed Hecke ...
Paul D. Nelson
doaj   +1 more source

MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS

Forum of Mathematics, Pi, 2013
Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function $f(q)$, Ramanujan claims that as $q$ approaches an even-order $2k$ root of unity, we have $$\begin{eqnarray ...
AMANDA FOLSOM, KEN ONO, ROBERT C. RHOADES   +2 more
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

On some automorphic properties of Galois traces of class invariants from generalized Weber functions of level 5

Open Mathematics, 2019
After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the ...
Eum Ick Sun, Jung Ho Yun
doaj   +1 more source

Eichler–Selberg relations for singular moduli

Forum of Mathematics, Sigma
The Eichler–Selberg trace formula expresses the trace of Hecke operators on spaces of cusp forms as weighted sums of Hurwitz–Kronecker class numbers. We extend this formula to a natural class of relations for traces of singular moduli, where one views ...
Yuqi Deng, Toshiki Matsusaka, Ken Ono
doaj   +1 more source

Deformations of Theta Integrals and A Conjecture of Gross-Zagier

Forum of Mathematics, Sigma
In this paper, we complete the proof of the conjecture of Gross and Zagier concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an analogue of the incoherent Eisenstein series over
Jan H. Bruinier, Yingkun Li, Tonghai Yang   +2 more
doaj   +1 more source

Combination of a triple wavelength (650 nm, 810 nm, and 915 nm) class IV laser system and local mechanical abrasion in the treatment of chronic toenail onychomycosis: an uncontrolled prospective pilot study. [PDF]

Int J Dermatol, 2022
Aukstikalnyte AE, Cibien E, De Demo P, Eisendle K.   +3 more
europepmc   +1 more source

Modular knots, automorphic forms, and the Rademacher symbols for triangle groups. [PDF]

Res Math Sci, 2023
Matsusaka T, Ueki J.
europepmc   +1 more source