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pro vyhledávání: '"11f11"'
We give Euler-like recursive formulas for the $t$-colored partition function when $t=2$ or $t=3,$ as well as for all $t$-regular partition functions. In particular, we derive an infinite family of ``triangular number" recurrences for the $3$-colored
Externí odkaz:
http://arxiv.org/abs/2412.14344
Autor:
Tajima, Ryota
For a normalized newform $g \in S_{k}(\Gamma_{0}(N))$ with complex multiplication by an imaginary quadratic field $K$, there is a mock modular form $F^{+}$ corresponding to $g$. K. Bringmann et al. modified $F^{+}$ in order to obtain a $p$-adic modul
Externí odkaz:
http://arxiv.org/abs/2412.12811
Our main result in this article is a proof (under mild technical assumptions) of an analogue for $p$-adic Galois representations attached to a newform $f$ of even weight $k\geq4$ of Kolyvagin's conjecture on the $p$-indivisibility of derived Heegner
Externí odkaz:
http://arxiv.org/abs/2412.02303
Let $T_m(N,2k)$ denote the $m$-th Hecke operator on the space $S_{2k}(\Gamma_0(N))$ of cuspidal modular forms of weight $2k$ and level $N$. In this paper, we study the non-repetition of the second coefficient of the characteristic polynomial of $T_m(
Externí odkaz:
http://arxiv.org/abs/2411.18419
Autor:
Branchereau, Romain
We define a theta lift between the homology in degree $N-1$ of a locally symmetric space associated to $\mathrm{SL}_N(\mathbb{R})$ and the space of modular forms of weight $N$. We show that the Fourier coefficients of this lift are Poincar\'e duals t
Externí odkaz:
http://arxiv.org/abs/2411.08690
We establish an unconditional result concerning the asymptotic formula for the moment of derivatives of $L$-functions $L(s, f \otimes \chi_{8d})L(s, g \otimes \chi_{8d})$ over quadratic twists, where $f$ and $g$ are distinct cuspidal newforms.
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Externí odkaz:
http://arxiv.org/abs/2411.07630
Autor:
Boylan, Matthew, Swati
We study the index of nilpotency relative to certain Hecke operators in spaces of modular forms with integer weight and level $N$ with integer coefficients modulo primes $p$ for $(p, N) \in \{(3, 1), (5, 1), (7, 1), (4, 3)\}$. In these settings, we p
Externí odkaz:
http://arxiv.org/abs/2410.24182
We investigate the question of when an eta quotient is a derivative of a formal power series with integer coefficients and present an analysis in the case of level 10. As a consequence, we establish and classify an infinite number of integral evaluat
Externí odkaz:
http://arxiv.org/abs/2410.19186
Autor:
Kumar, Arvind, Mishra, Prabhat Kumar
Let $k \ge 2$ be an even integer, $ \ell \ge \max\{5, k-1\} $ be a prime, and $N$ be a squarefree positive integer. It is known that if the $\rm{mod}\,\ell$ Galois representation $\overline{\rho}_f$ associated with a newform $f$ of weight $k$, level
Externí odkaz:
http://arxiv.org/abs/2410.16854
Autor:
Besrour, Khalil, Sebbar, Abdellah
In this paper, we explore the modular differential equation $\displaystyle y'' + F(z)y = 0$ on the upper half-plane $\mathbb{H}$, where $F$ is a weight 4 modular form for $\Gamma_0(2)$. Our approach centers on solving the associated Schwarzian equati
Externí odkaz:
http://arxiv.org/abs/2410.14006