On the gaps of the Lagrange spectrum
On the Gaps of the Markoff Spectrum.
On the Gaussian Markoff spectrum.
On the Gelfond-Feldman measure of algebraic independence
On the generalization of the D. H. Lehmer problem II
On the generalization of the Fibonacci-coefficient polynomials.
On the generalized Bernoulli numbers that belong to unequal characters.
The study of class number invariants of absolute abelian fields, the investigation of congruences for special values of L-functions, Fourier coefficients of half-integral weight modular forms, Rubin's congruences involving the special values of L-functions of elliptic curves with complex multiplication, and many other problems require congruence properties of the generalized Bernoulli numbers (see [16]-[18], [12], [29], [3], etc.). The first steps in this direction can be found in the papers of...
On the generalized Davenport constant and the Noether number
Known results on the generalized Davenport constant relating zero-sum sequences over a finite abelian group are extended for the generalized Noether number relating rings of polynomial invariants of an arbitrary finite group. An improved general upper degree bound for polynomial invariants of a non-cyclic finite group that cut out the zero vector is given.
On the generalized Fermat equation over totally real fields
In a recent paper, Freitas and Siksek proved an asymptotic version of Fermat’s Last Theorem for many totally real fields. We prove an extension of their result to generalized Fermat equations of the form , where A, B, C are odd integers belonging to a totally real field.
On the generalized principal ideal theorem of complex multiplication
In the -th cyclotomic field a prime number, , the prime is totally ramified and the only ideal above is generated by , with the primitive -th root of unity . Moreover these numbers represent a norm coherent set, i.e. . It is the aim of this article to establish a similar result for the ray class field of conductor over an imaginary quadratic number field where is the power of a prime ideal in . Therefore the exponential function has to be replaced by a suitable elliptic function....
On the generalized Ramanujan-Nagell equation I
On the generalized Ramanujan-Nagell equation, II
On the generalized Ramanujan-Nagell equation
On the Generating Functions of Certain Eisenstein Series.
On the Generation of Dyadic Integral Orthogonal Groups.
On the generation of the coefficient field of a newform by a single Hecke eigenvalue
Let be a non-CM newform of weight . Let be a subfield of the coefficient field of . We completely settle the question of the density of the set of primes such that the -th coefficient of generates the field . This density is determined by the inner twists of . As a particular case, we obtain that in the absence of nontrivial inner twists, the density is for equal to the whole coefficient field. We also present some new data on reducibility of Hecke polynomials, which suggest questions...
On the genus group of algebraic number fields
On the Genus of Norm Forms.
On the Geometry of a Siegel Modular Threefold.
On the Goldbach conjecture and the consistency of general recursive arithemetic.