Number Theory and Applications

1. Front Matter

   Pages i-xi

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2. Analysis of the Lattice Sieve

   • R. Balasubramanian, Gagan Garg, C. E. Veni Madhavan

   Pages 1-13

3. 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

   • Ioulia Baoulina

   Pages 15-24

4. On the Sign Changes of Hecke Eigenvalues

   • Y. J. Choie, A. Sankaranarayanan, J. Sengupta

   Pages 25-32

5. Distribution of Some Sequences Modulo 1

   • Artūras Dubickas

   Pages 33-41

6. Large Sieves and Cusp Forms of Weight One

   • Satadal Ganguly

   Pages 43-54

7. Open Problems on Densities

   • Georges Grekos

   Pages 55-63

8. A Geometric Framework for the Subfield Problem of Generic Polynomials Via Tschirnhausen Transformation

   • Akinari Hoshi, Katsuya Miyake

   Pages 65-104

9. On q-Additive and q-Multiplicative Functions

   • I. Kátai

   Pages 105-126

10. Variations of the Sato-Tate Conjecture

    • M. Ram Murty

    Pages 127-138

11. On the Determination of Diophantine Triples

    • D. S. Nagaraj, Parvati Shastri

    Pages 139-148

12. On the Clique and the Chromatic Numbers of High-Dimensional Distance Graphs

    • A. M. Raigorodskii, O. I. Rubanov

    Pages 149-155

13. On Units Generated by Euler Systems

    • Anupam Saikia

    Pages 157-174

14. Pillai’s Problem on Consecutive Integers

    • N. Saradha, R. Thangadurai

    Pages 175-188

15. Characterization of Class Groups of Krull Monoids Via Their Systems of Sets of Lengths: A Status Report

    • Wolfgang A. Schmid

    Pages 189-212

16. Diophantine Approximation by Numbers of Small Height

    • W. M. Schmidt

    Pages 213-218

17. Theory of the Siegel Modular Variety

    • Jae-Hyun Yang

    Pages 219-278

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.

• Harish-Chandra Research Inst., Allahabad, India

  S. D. Adhikari, B. Ramakrishnan

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