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.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

Readership

Graduate students and research mathematicians interested in number theory.

Table of Contents

• R. Balasubramanian, G. Garg, and C. E. Veni Madhavan -- Analysis of the lattice sieve 1
• I. Baoulina -- On the number of solutions to the equation $(x_{1} +\dots X_{n})^{m}=ax_{1}\dots x_{n}$ over the finite field $F_q$ for $gcd(m-n, q-1)=7$ and $gcd(m-n, q-1)=14$
• Y. J. Choie, A. Sankaranarayanan, and J. Sengupta -- On the sign changes of Hecke eigenvalues
• A. Dubickas -- Distribution of some sequences modulo 1
• S. Ganguly -- Large sieves and cusp forms of weight one
• G. Grekos -- Open problems on densities
• A. Hoshi and K. Miyake -- A geometric framework for the subfield problem of generic polynomials via Tschirnhausen transformation
• I. Kátai -- On $q$-additive and $q$-multiplicative functions
• M. R. Murty -- Variations of the Sato-Tate conjecture
• D. S. Nagaraj and P. Sastri -- On the determination of Diophantine triples
• A. M. Raigorodskii and O. I. Rubanov -- On the clique and the chromatic numbers of high-dimensional distance graphs
• A. Saikia -- On units generated by Euler systems
• N. Saradha and R. Thangadurai -- Pillai's problem on consecutive integers
• W. A. Schmid -- Characterization of class groups of Krull monoids via their systems of sets of lengths: A status report
• W. M. Schmidt -- Diophantine approximation by numbers of small height
• J.-H. Yang -- Theory of the Siegel modular variety