Results 11 to 20 of about 6,212 (114)
Fourier expansion of light‐cone Eisenstein series
Journal of the London Mathematical Society, Volume 108, Issue 6, Page 2175-2247, December 2023., 2023 Abstract In this work, we give an explicit formula for the Fourier coefficients of Eisenstein series corresponding to certain arithmetic lattices acting on hyperbolic n+1$n+1$‐space. As a consequence, we obtain results on location of all poles of these Eisenstein series as well as their supremum norms.
Dubi Kelmer, Shucheng Yu
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Aspects of the screw function corresponding to the Riemann zeta‐function
Journal of the London Mathematical Society, Volume 108, Issue 4, Page 1448-1487, October 2023., 2023 Abstract We introduce a screw function corresponding to the Riemann zeta‐function and study its properties from various aspects. Typical results are several equivalent conditions for the Riemann hypothesis in terms of the screw function. One of them can be considered an analog of so‐called Weil's positivity or Li's criterion.
Masatoshi Suzuki
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Monodromy of four‐dimensional irreducible compatible systems of Q$\mathbb {Q}$
Bulletin of the London Mathematical Society, Volume 55, Issue 4, Page 1773-1790, August 2023., 2023 Abstract Let F$F$ be a totally real field and n⩽4$n\leqslant 4$ a natural number. We study the monodromy groups of any n$n$‐dimensional strictly compatible system {ρλ}λ$\lbrace \rho _\lambda \rbrace _\lambda$ of λ$\lambda$‐adic representations of F$F$ with distinct Hodge–Tate numbers such that ρλ0$\rho _{\lambda _0}$ is irreducible for some λ0$\lambda ...
Chun Yin Hui
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Mathematika, Volume 69, Issue 1, Page 250-285, January 2023., 2023 Abstract We introduce a class of multiplicative functions in which each function satisfies some statistic conditions, and then prove that the above functions are not correlated with finite degree polynomial nilsequences. Besides, we give two applications of this result. One is that the twisting of coefficients of automorphic L‐function on GLm(m⩾2)$GL_m
Xiaoguang He, Mengdi Wang
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Airy sheaves for reductive groups
Proceedings of the London Mathematical Society, Volume 126, Issue 1, Page 390-428, January 2023., 2023 Abstract We construct a class of ℓ$\ell$‐adic local systems on A1$\mathbb {A}^1$ that generalizes the Airy sheaves defined by N. Katz to reductive groups. These sheaves are finite field analogues of generalizations of the classical Airy equation y′′(z)=zy(z)$y^{\prime \prime }(z)=zy(z)$. We employ the geometric Langlands correspondence to construct the
Konstantin Jakob +2 more
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A density theorem for Sp(4)$\operatorname{Sp}(4)$
Journal of the London Mathematical Society, Volume 105, Issue 4, Page 2047-2075, June 2022., 2022 Abstract Strong bounds are obtained for the number of automorphic forms for the group Γ0(q)⊆Sp(4,Z)$\Gamma _0(q) \subseteq \operatorname{Sp}(4,\mathbb {Z})$ violating the Ramanujan conjecture at any given unramified place, which go beyond Sarnak's density hypothesis.
Siu Hang Man
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The false theta functions of Rodgers and their modularity
Bulletin of the London Mathematical Society, Volume 53, Issue 4, Page 963-980, August 2021., 2021 Abstract In this survey article, we explain how false theta functions can be embedded into a modular framework and show some of the applications of this modularity.
Kathrin Bringmann
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Campana points of bounded height on vector group compactifications
Proceedings of the London Mathematical Society, Volume 123, Issue 1, Page 57-101, July 2021., 2021 Abstract We initiate a systematic quantitative study of subsets of rational points that are integral with respect to a weighted boundary divisor on Fano orbifolds. We call the points in these sets Campana points. Earlier work of Campana and subsequently Abramovich shows that there are several reasonable competing definitions for Campana points.
Marta Pieropan +3 more
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On modeling and identification of empirical partially intelligible white noise processes
Asian Journal of Control, Volume 23, Issue 3, Page 1262-1279, May 2021., 2021 Abstract The paper discusses the identification of the empirical, partially intelligible white noise processes generated by deterministic numerical algorithms. The introduced fuzzy‐random complementary approach can identify the inner hidden correlational patterns of the empirical white noise process if the process has a real hidden structure of this ...
Péter Várlaki +2 more
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Toroidal automorphic forms, Waldspurger periods and double Dirichlet series
, 2011 The space of toroidal automorphic forms was introduced by Zagier in the 1970s: a GL_2-automorphic form is toroidal if it has vanishing constant Fourier coefficients along all embedded non-split tori. The interest in this space stems (amongst others) from
Alain Connes +14 more
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