Zobrazeno 1 - 10
of 602
pro vyhledávání: '"11l05"'
Autor:
Assing, Edgar
We prove new bounds for the Fourier coefficients of Jacobi forms using a method of Iwaniec. In view of the Fourier-Jacobi expansion of degree two Siegel modular forms, we can use these to obtain strong bounds on fundamental Fourier coefficients of Si
Externí odkaz:
http://arxiv.org/abs/2411.00450
Autor:
Mujdei, Catinca
We study Kloosterman sums on the orthogonal groups $SO_{3,3}$ and $SO_{4,2}$, associated to short elements of their respective Weyl groups. An explicit description for these sums is obtained in terms of multi-dimensional exponential sums. These are b
Externí odkaz:
http://arxiv.org/abs/2410.20569
Autor:
Kwan, Chung-Hang, Leung, Wing Hong
In this article, we provide a "beyond-endoscopic" treatment of the functional equations for standard $L$-functions, building on ideas and techniques from Venkatesh's thesis and "spectral reciprocity".
Externí odkaz:
http://arxiv.org/abs/2410.16921
Autor:
Kwan, Chung-Hang, Leung, Wing Hong
In this article, we examine the role of the recent banner of Spectral Reciprocity within the Langlands Beyond Endoscopy and Braverman-Kazhdan programmes. We present a novel four-variable character sum identity, which serves as a pivotal arithmetic in
Externí odkaz:
http://arxiv.org/abs/2410.11193
We study the non-vanishing problem for the family of Hecke $L$-functions associated to primitive cubic characters defined over the Eisenstein quadratic number field $\mathbb{Q}(\omega)$. We prove unconditionally that a positive proportion of Hecke $L
Externí odkaz:
http://arxiv.org/abs/2410.03048
Autor:
Leung, Sun-Kai
Given a large smooth conductor, we establish the nonvanishing of the central values for at least $35.9\%$ of the primitive Dirichlet $L$-functions.
Comment: 11 pages
Comment: 11 pages
Externí odkaz:
http://arxiv.org/abs/2410.01713
If the standard 1D quantum infinite potential well initially in its ground state suffers a sudden expansion, it turns out that in the evolution of the system they may appear plateaux of probability for some fractional times, as noticed by C. Aslangul
Externí odkaz:
http://arxiv.org/abs/2409.06058
In this paper we obtain explicit formulas for the traces of Hecke operators on spaces of cusp forms in certain instances related to arithmetic triangle groups. These expressions are in terms of hypergeometric character sums over finite fields, a theo
Externí odkaz:
http://arxiv.org/abs/2408.02918
Autor:
Ye, Zhaoxi, Xu, Zhefeng
Let $j \ge1$, $k\ge 0$ be real numbers and $\varphi(n)$ be the Euler function. In this paper, we study the asymptotical behaviour of the summation function $$S_{j,k}(x):=\sum_{n\le x}\frac{\varphi\left ( \left [ \frac{x}{n} \right ]^{j} \right ) }{\l
Externí odkaz:
http://arxiv.org/abs/2408.01015
Autor:
Zhu, Xiao-Jie
We give an explicit formula for dimensions of spaces of rational-weight modular forms whose multiplier systems are induced by eta-quotients of fractional exponents. As the first application, we give series expressions of Fourier coefficients of the $
Externí odkaz:
http://arxiv.org/abs/2408.00246