Number Theory and Applications : Proceedings of the International Conferences on Number Theory and Cryptography

This collection of articles contains the proceedings of the two international conferences (on Number Theory and Cryptography) held at the Harish - Chandra Research Institute. In recent years the interest in number theory has increased due to its applications in areas like error-correcting codes and cryptography. These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. While some papers do contain new results, several of the papers are expository articles that mention open questions, which will be useful to young researchers. Front Matter....Pages i-xi Analysis of the Lattice Sieve....Pages 1-13 On the Number of Solutions to the Equation (x1 + ⋯ + x n ) m = ax1 ⋯ x n over the Finite Field \( \mathbb{F} \) q for gcd(m − n, q − 1) = 7 and gcd(m − n, q − 1) = 14....Pages 15-24 On the Sign Changes of Hecke Eigenvalues....Pages 25-32 Distribution of Some Sequences Modulo 1....Pages 33-41 Large Sieves and Cusp Forms of Weight One....Pages 43-54 Open Problems on Densities....Pages 55-63 A Geometric Framework for the Subfield Problem of Generic Polynomials Via Tschirnhausen Transformation....Pages 65-104 On q-Additive and q-Multiplicative Functions....Pages 105-126 Variations of the Sato-Tate Conjecture....Pages 127-138 On the Determination of Diophantine Triples....Pages 139-148 On the Clique and the Chromatic Numbers of High-Dimensional Distance Graphs....Pages 149-155 On Units Generated by Euler Systems....Pages 157-174 Pillai’s Problem on Consecutive Integers....Pages 175-188 Characterization of Class Groups of Krull Monoids Via Their Systems of Sets of Lengths: A Status Report....Pages 189-212 Diophantine Approximation by Numbers of Small Height....Pages 213-218 Theory of the Siegel Modular Variety....Pages 219-278