On the first case of Fermat's last theorem.
On the First Case of Fermat's Last Theorem, II.
On the first power mean of -functions with the weight of general Kloosterman sums.
On the first sign change in Mertens' theorem
The function is known to change sign infinitely often, but so far all calculated values are positive. In this paper we prove that the first sign change occurs well before exp(495.702833165).
On the Fourier coefficients of modular forms
On the Fourier coefficients of modular forms. II.
On the Fourier coefficients of small positive powers of 0 ... .
On the Fourier expansions of Jacobi forms.
On the Fourier expansions of Jacobi forms of half-integral weight.
On the Fourth Moment of the Riemann Zeta Functions
On the fractional parts of cubic forms
On the fractional parts of the natural powers of a fixed number.
On the fractional parts of the powers of a rational number
On the fractional parts of and related sequences. I
This paper and its sequels deal with a new concept of distributions modulo one which is connected with the Dirichlet divisor and similar problems. Each of the theorems has some independent interest, and in addition some of the techniques developed lead to improvements in certain applications of the hyperbola method.
On the fractional parts of and related sequences. II
As promised in the first paper of this series (Ann. Inst. Fourier, 26-4 (1976), 115-131), these two articles deal with the asymptotic distribution of the fractional parts of where is an arithmetical function (namely , , ) and is an integer (or a prime order) running over the interval . The results obtained are rather sharp, although one can improve on some of them at the cost of increased technicality. Number-theoretic applications will be given later on.
On the frequencies of large values of divisor functions
On the frequency of small fractional parts in certain real sequences, IV
On the frequency of Titchmarsh's phenomenon for ζ(s). VI
On the Frobenius number of a modular Diophantine inequality
We present an algorithm for computing the greatest integer that is not a solution of the modular Diophantine inequality , with complexity similar to the complexity of the Euclid algorithm for computing the greatest common divisor of two integers.
On the Frobenius number of a proportionally modular Diophantine inequality.