A Survey of Lattice-Based Physical-Layer Security for Wireless Systems with p-Modular Lattice Constructions [PDF]
EntropyPhysical-layer security (PLS) provides an information-theoretic framework for securing wireless communications by exploiting channel and signal-structure asymmetries, thereby avoiding reliance on computational hardness assumptions.
Hassan Khodaiemehr +5 more
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Siegel theta series for indefinite quadratic forms [PDF]
Research in Number Theory, 2021 AbstractThe modular transformation behavior of theta series for indefinite quadratic forms is well understood in the case of elliptic modular forms due to Vignéras, who deduced that solving a differential equation of second order serves as a criterion for modularity. In this paper, we will give a generalization of this result to Siegel theta series.
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Indefinite theta series and generalized error functions [PDF]
Selecta Mathematica, 2018 32 pages, 2 figures; v2: discussed $\Delta_{12}=0$ case at end of section 3, added subsection 4.4 on $C_1=C_2$ case (relevant for signature (2,1)), and added several references; v3: published version in Selecta Mathematica (with apologies for not uploading it earlier)
Alexandrov, Sergey +3 more
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Universal Triple Massey Products on Elliptic Curves and Hecke's Indefinite Theta Series [PDF]
Moscow Mathematical Journal, 2005 19 ...
Pasol, Vicentiu, Polishchuk, Alexander
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An algebraic property of Hecke operators and two indefinite theta series [PDF]
Forum Mathematicum, 2013 Abstract We prove an algebraic property of the elements defining Hecke operators on period polynomials associated with modular forms, which implies that the pairing on period polynomials corresponding to the Petersson scalar product of modular forms is Hecke equivariant.
Vicentiu Pasol, Alexandru A. Popa
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Elliptic and Siegel Theta Series for Indefinite Quadratic Forms
, 2022 In this thesis, we embed four research articles on elliptic and Siegel theta series for indefinite quadratic forms. In the first two articles, we generalize results on elliptic theta series to Siegel theta series, i.e. theta series for arbitrary genus $n\in \N$.
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Squashed toric manifolds and higher depth mock modular forms
Journal of High Energy Physics, 2019 Squashed toric sigma models are a class of sigma models whose target space is a toric manifold in which the torus fibration is squashed away from the fixed points so as to produce a neck-like region.
Rajesh Kumar Gupta +2 more
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$r$-tuple error functions and indefinite theta series of higher-depth [PDF]
Communications in Number Theory and Physics, 2018 22 pages; v2: Typos ...
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Theta series for indefinite quadratic forms over real number fields [PDF]
Acta Arithmetica, 1995 The goal is the construction of a theta series for a general quadratic from \(q\) and lattice \(L\) over a real algebraic number field. The first difficulty is that \(L\) need not be free: but the Scharlau transfer \(\text{tr} (q)\) lies over \(\mathbb{Q}\) and \(L\) is free as a \(\mathbb{Z}\)-module.
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Indefinite theta series of signature (1,1) from the point of view of homological mirror symmetry
Advances in Mathematics, 2000 We apply the homological mirror symmetry for elliptic curves to the study of indefinite theta series. We prove that every such series corresponding to a quadratic form of signature (1,1) can be expressed in terms of theta series associated with split quadratic forms and the usual theta series.
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