Generalized Catalan numbers: linear recursion and divisibility.
Generalized Catalan numbers. (Nombres de Catalan généralisés.)
Generalized Cauchy determinants.
Generalized continued fractions and orbits under the action of Hecke triangle groups
Generalized convolution identities for Stirling numbers of the second kind.
Generalized Dedekind sums.
Generalized Dedekind sums, correlation of L-series, and the Galois module of cot(π/N)cot(mπ/N)
Generalized divisor problem.
Generalized divisor problem for new forms of higher level
Suppose that is a primitive Hecke eigenform or a Mass cusp form for with normalized eigenvalues and let be a real number. We consider the sum and show that for every and . The same problem was considered for the case , that is for the full modular group in Lü (2012) and Kanemitsu et al. (2002). We consider the problem in a more general setting and obtain bounds which are better than those obtained by the classical result of Landau (1915) for . Since the result is valid for arbitrary...
Generalized Dumont-Foata polynomials and alternative tableaux.
Generalized Eisenstein series and modified Dedekind sums.
Generalized Eta-Functions and Certain Ray Class Invariants of Real Quadratic Fields.
Generalized Eulerian numbers combinatorial applications.
Generalized Frobenius numbers: bounds and average behavior
Generalized Frobenius partitions, k-cores, k-quotients, and cranks
Generalized golden ratios of ternary alphabets
Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases in dependence...
Generalized Hecke groups and Hecke polygons.
Generalized Hilbert fields.
Generalized Hubert fields, II
Generalized Iwasawa invariants in a family