Slightly improved sum-product estimates in fields of prime order
Slim exceptional sets for sums of fourth and fifth powers
Slope filtrations revisited.
Slopes of modular forms and congruences
Our aim in this paper is to prove congruences between on the one hand certain eigenforms of level and weight greater than 2 and on the other hand twists of eigenforms of level and weight 2. One knows a priori that such congruences exist; the novelty here is that we determine the character of the form of weight 2 and the twist in terms of the slope of the higher weight form, i.e., in terms of the valuation of its eigenvalue for . Curiously, we also find a relation between the leading terms of...
Slopes of modular forms and congruences
Sloping binary numbers: a new sequence related to the binary numbers.
Slowly growing sequences and discrepancy modulo one
Small digitwise perturbations of a number make it normal to unrelated bases.
Small discriminants of complex multiplication fields of elliptic curves over finite fields
We obtain a conditional, under the Generalized Riemann Hypothesis, lower bound on the number of distinct elliptic curves over a prime finite field of elements, such that the discriminant of the quadratic number field containing the endomorphism ring of over is small. For almost all primes we also obtain a similar unconditional bound. These lower bounds complement an upper bound of F. Luca and I. E. Shparlinski (2007).
Small eigenvalues of Laplacian for
Small exponent point groups on elliptic curves
Let be an elliptic curve defined over , the finite field of elements. We show that for some constant depending only on , there are infinitely many positive integers such that the exponent of , the group of -rational points on , is at most . This is an analogue of a result of R. Schoof on the exponent of the group of -rational points, when a fixed elliptic curve is defined over and the prime tends to infinity.
Small gaps between zeros of twisted L-functions
Small gaps in coefficients of -functions and -free numbers in short intervals.
Small generators of function fields
Let be a finite extension of a global field. Such an extension can be generated over by a single element. The aim of this article is to prove the existence of a ”small” generator in the function field case. This answers the function field version of a question of Ruppert on small generators of number fields.
Small limit points of Mahler's measure.
Small Linearly Independent Zeros of Quadratic Forms.
Small maximal sum-free sets.
Small points and Arakelov theory.
Small points on a multiplicative group and class number problem
Let be an algebraic subvariety of a torus and denote by the complement in of the Zariski closure of the set of torsion points of . By a theorem of Zhang, is discrete for the metric induced by the normalized height . We describe some quantitative versions of this result, close to the conjectural bounds, and we discuss some applications to study of the class group of some number fields.
Small prime solutions of linear ternary equations