Results 1 to 10 of about 66 (66)

On average theta functions of certain quadratic forms as sums of Eisenstein series

Open Mathematics, 2023
Let QQ be an integral positive definite quadratic form of level NN in 2k2k variables. Further, we assume that (−1)kN{\left(-1)}^{k}N is a fundamental discriminant. We express the average theta function of QQ as an explicit sum of Eisenstein series, which
Eum Ick Sun
doaj   +1 more source

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

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
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

THE MOONSHINE MODULE FOR CONWAY’S GROUP

Forum of Mathematics, Sigma, 2015
We exhibit an action of Conway’s group – the automorphism group of the Leech lattice – on a distinguished super vertex operator algebra, and we prove that the associated graded trace functions are normalized principal moduli, all having vanishing ...
JOHN F. R. DUNCAN, SANDER MACK-CRANE
doaj   +1 more source

STARK POINTS AND $p$-ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE

Forum of Mathematics, Pi, 2015
Let $E$ be an elliptic curve over $\mathbb{Q}$, and let ${\it\varrho}_{\flat }$ and ${\it\varrho}_{\sharp }$ be odd two-dimensional Artin representations for which ${\it\varrho}_{\flat }\otimes {\it\varrho}_{\sharp }$ is self-dual.
HENRI DARMON, ALAN LAUDER, VICTOR ROTGER
doaj   +1 more source

Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52

Open Mathematics, 2017
The convolution sum, ∑(l,m)∈N02αl+βm=nσ(l)σ(m), $ \begin{array}{} \sum\limits_{{(l\, ,m)\in \mathbb{N}_{0}^{2}}\atop{\alpha \,l+\beta\, m=n}} \sigma(l)\sigma(m), \end{array} $ where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms
Ntienjem Ebénézer
doaj   +1 more source

Evaluation of the convolution sums ∑al+bm=n lσ(l) σ(m) with ab ≤ 9

Open Mathematics, 2017
The generating functions of divisor functions are quasimodular forms of weight 2 and their products belong to a space of quasimodular forms of higher weight.
Park Yoon Kyung
doaj   +1 more source

Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8

Open Mathematics
In this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered.
Jin Seokho, Park Ho
doaj   +1 more source