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.
On the Graded Ring of Hubert Modular Forms Associated with Q (|..5).
On the graded rings of modular forms
On the greatest prime divisor of quadratic sequences
On the greatest prime factor of for a prime p and other expressions
On the greatest prime factor of a cubic polynomial.
On the greatest prime factor of
On the greatest prime factor of (ab + 1) (ac + 1) (bc + 1)
On the greatest prime factor of (ab + 1)(bc + 1)(ca + 1)
On the greatest prime factor of an arithmetical progression. II
On the greatest prime factor of Markov pairs
On the greatest prime factor of
There exist infinitely many integers such that the greatest prime factor of is at least . The proof is a combination of Hooley’s method – for reducing the problem to the evaluation of Kloosterman sums – and the majorization of Kloosterman sums on average due to the authors.