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of 31
pro vyhledávání: '"Man, Siu Hang"'
Autor:
Kala, Vítězslav, Man, Siu Hang
We establish a new connection between sails, a key notion in the geometric theory of generalised continued fractions, and arithmetic of totally real number fields, specifically, universal quadratic forms and additively indecomposable integers. Our ma
Externí odkaz:
http://arxiv.org/abs/2403.18390
We show that if a universal quadratic form exists over an infinite degree, totally real extension of the field of rationals $\mathbb{Q}$, then the set of totally positive integers in the extension does not have the Northcott property. In particular,
Externí odkaz:
http://arxiv.org/abs/2308.16721
Autor:
Man, Siu Hang
Publikováno v:
Adv. Math. 447 (2024) 109694
We establish an upper bound on the number of real multiquadratic fields that admit a universal quadratic lattice of a given rank, or contain a given amount of indecomposable elements modulo totally positive units, obtaining density zero statements. W
Externí odkaz:
http://arxiv.org/abs/2307.04908
Autor:
Man, Siu Hang
For a partition $\lambda \vdash n$, we let $\operatorname{pd}(\lambda)$, the parity difference of $\lambda$, to be the number of odd parts of $\lambda$ minus the number of even parts of $\lambda$. We show that as $n\to \infty$, the normalised parity
Externí odkaz:
http://arxiv.org/abs/2306.11909
For a random partition, one of the most basic questions is: what can one expect about the parts which arise? For example, what is the distribution of the parts of random partitions modulo $N$? Since most partitions contain a $1$, and indeed many $1$s
Externí odkaz:
http://arxiv.org/abs/2305.02928
Recently, much attention has been given to various inequalities among partition functions. For example, Nicolas, {and later DeSavlvo--Pak,} proved that $p(n)$ is eventually log-concave, and Ji--Zang showed that the cranks are eventually unimodal. Thi
Externí odkaz:
http://arxiv.org/abs/2209.12239
Autor:
Man, Siu Hang
Publikováno v:
In Advances in Mathematics June 2024 447
Autor:
Man, Siu Hang
Strong bounds are obtained for the number of automorphic forms for the group $\Gamma_0(q) \subseteq \operatorname{Sp}(4,\mathbb{Z})$ violating the Ramanujan conjecture at any given unramified place, which go beyond Sarnak's density hypothesis. The pr
Externí odkaz:
http://arxiv.org/abs/2101.09602
Autor:
Man, Siu Hang
Publikováno v:
Ramanujan J. 57 (2022), 707-753
We prove power-saving bounds for general Kloosterman sums on $\operatorname{Sp}(4)$ associated to all Weyl elements via a stratification argument coupled with $p$-adic stationary phase methods. We relate these Kloosterman sums to the Fourier coeffici
Externí odkaz:
http://arxiv.org/abs/2006.03036
Autor:
Man, Siu Hang
Publikováno v:
Acta. Arith. 213 (2024) 227-271
We compute explicit formulae for the constant terms and Fourier coefficients for Eisenstein series on $\operatorname{Sp}(4,\mathbb{R})$, in terms of zeta functions and Whittaker functions. We also develop a generalisation of Ramanujan sums to $\opera
Externí odkaz:
http://arxiv.org/abs/2003.06890