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1.
Hugh Thomas 《Order》2006,23(2-3):249-269
In this paper, we study lattices that posess both the properties of being extremal (in the sense of Markowsky) and of being left modular (in the sense of Blass and Sagan). We call such lattices trim and show that they posess some additional appealing properties, analogous to those of a distributive lattice. For example, trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice is contractible or homotopic to a sphere; the latter holds exactly if the maximum element of the lattice is a join of atoms. Any distributive lattice is trim, but trim lattices need not be graded. The main example of ungraded trim lattices are the Tamari lattices and generalizations of them. We show that the Cambrian lattices in types A and B defined by Reading are trim; we conjecture that all Cambrian lattices are trim. 相似文献
2.
Mihran Papikian 《Transactions of the American Mathematical Society》2007,359(7):3483-3503
Under a certain assumption, similar to Manin's conjecture, we prove an upper bound on the degree of modular parametrizations of elliptic curves by Drinfeld modular curves, which is the function field analogue of the conjectured bound over the rational numbers.
3.
Modular and quasimodular solutions of a specific second order differential equation in the upper-half plane, which originates from a study of supersingular j-invariants in the first author's work with Don Zagier, are given explicitly. Positivity of Fourier coefficients of some of the solutions as well as a characterization of the differential equation are also discussed. 相似文献
4.
5.
Anna Avallone 《Mathematica Slovaca》2007,57(2):129-140
We prove the existence of separating points for every countable family of nonatomic σ-additive modular measures on a σ-complete lattice ordered effect algebra.
相似文献
6.
7.
In this paper, we deal with the critical problems in residue arithmetic. The reverse conversion from a Residue Number System (RNS) to positional notation is a main non-modular operation, and it constitutes a basis of other non-modular procedures used to implement various computational algorithms. We present a novel approach to the parallel reverse conversion from the residue code into a weighted number representation in the Mixed-Radix System (MRS). In our proposed method, the calculation of mixed-radix digits reduces to a parallel summation of the small word-length residues in the independent modular channels corresponding to the primary RNS moduli. The computational complexity of the developed method concerning both required modular addition operations and one-input lookup tables is estimated as , where k equals the number of used moduli. The time complexity is modular clock cycles. In pipeline mode, the throughput rate of the proposed algorithm is one reverse conversion in one modular clock cycle. 相似文献
8.
We derive many new identities involving the Ramanujan-Göllnitz-Gordon continued fraction H(q). These include relations between H(q) and H(q
n
) , which are established using modular equations of degree n. We also evaluate explicitly H(q) at
for various positive integers n. Using results of M. Deuring, we show that
are units for all positive integers n. 相似文献
9.
Shan Wen WANG 《数学学报(英文版)》2021,37(1):173-204
This article is the second article on the generalization of Kato's Euler system. The main subject of this article is to construct a family of Kato's Euler systems over the cuspidal eigencurve, which interpolate the Kato's Euler systems associated to the modular forms parametrized by the cuspidal eigencurve. We also explain how to use this family of Kato's Euler system to construct a family of distributions on Zp over the cuspidal eigencurve; this distribution gives us a two-variable p-adic L function which interpolate the p-adic L function of modular forms. 相似文献
10.
P. Guerzhoy 《The Ramanujan Journal》2006,12(3):349-358
Faber polynomials appear when weight zero Hecke operators act on the modular j-invariant. They are polynomials in j with rational integral coefficents. Using the theory of p-adic modular forms we establish some congruences and divisibilities for these coefficients.
2000 Mathematics Subject Classification Primary—11F33
Supported by NSF grant DMS-0501225. 相似文献