Results 1 to 10 of about 327 (36)
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 +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
A Short Note on the Bruinier-Kohnen Sign Equidistribution Conjecture and Hal\'asz' Theorem [PDF]
, 2015 In this note, we improve earlier results towards the Bruinier-Kohnen sign equidistribution conjecture for half-integral weight modular eigenforms in terms of natural density by using a consequence of Hal\'asz' Theorem.
Inam, Ilker, Wiese, Gabor
core +3 more sources
Asymptotic expansions, $L$-values and a new Quantum Modular Form [PDF]
, 2013 In 2010 Zagier introduced the notion of a quantum modular form. One of his first examples was the "strange" function $F(q)$ of Kontsevich. Here we produce a new example of a quantum modular form by making use of some of Ramanujan's mock theta functions ...
Costa, Edgar +2 more
core +3 more sources
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 +2 more
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 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
q-hypergeometric double sums as mock theta functions [PDF]
, 2012 Recently, Bringmann and Kane established two new Bailey pairs and used them to relate certain q-hypergeometric series to real quadratic fields. We show how these pairs give rise to new mock theta functions in the form of q-hypergeometric double sums ...
Andrews +5 more
core +3 more sources
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
Partial theta functions and mock modular forms as q-hypergeometric series [PDF]
, 2011 Ramanujan studied the analytic properties of many $q$-hypergeometric series. Of those, mock theta functions have been particularly intriguing, and by work of Zwegers, we now know how these curious $q$-series fit into the theory of automorphic forms.
Bringmann, Kathrin +2 more
core +1 more source