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Arithmetic fundamental lemma for the spherical Hecke algebra
We define Hecke correspondences and Hecke operators on unitary RZ spaces and study their basic geometric properties, including a commutativity...
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Distribution of angles to lattice points seen from a fast moving observer
We consider a square expanding with constant speed seen from an observer moving away with constant acceleration and study the distribution of angles...
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The relatively perfect Greenberg transform and cycle class maps
Given a scheme over a complete discrete valuation ring of mixed characteristic with perfect residue field, the Greenberg transform produces a new...
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Pureté de l’approximation forte sur le corps des fonctions d’une courbe algébrique complexe
Over the function field of a complex algebraic curve, strong approximation off a non-empty finite set of places holds for the complement of a...
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Right-angled triangles with almost prime hypotenuse
The sequence OEIS A281505 consists of distinct odd legs in right triangles with integer sides and prime hypotenuse. In this paper, we count the...
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On p-adic Siegel–Eisenstein series from a point of view of the theory of mod \(p^m\) singular forms
We show that the p -adic Siegel–Eisenstein series of general degree attached to two kind of number sequences are both linear combinations of genus...
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Quadratic points on dynamical modular curves
Among all the dynamical modular curves associated to quadratic polynomial maps, we determine which curves have infinitely many quadratic points. This...
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An inclusion–exclusion principle for tautological sheaves on Hilbert schemes of points
We show an equation of Euler characteristics of tautological sheaves on Hilbert schemes of points on the fibers of a double point degeneration. This...
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Periodicity and pure periodicity in alternate base systems
We study the Cantor real base numeration system which is a common generalization of two positional systems, namely the Cantor system with a sequence...
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Ratios conjecture for quadratic twists of modular L-functions
We develop the L -functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic twist of...
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A rigidity theorem for self-expanders
In this paper, we completely classify 3-dimensional complete self-expanders with constant squared norm S of the second fundamental form and constant
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