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# Geometry, Algebra, Number Theory, and Their Information Technology Applications

• Kartonierter Einband
• 536 Seiten
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This volume contains proceedings of two conferences held in Toronto (Canada) and Kozhikode (India) in 2016 in honor of the 60th bi... Weiterlesen
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## Beschreibung

This volume contains proceedings of two conferences held in Toronto (Canada) and Kozhikode (India) in 2016 in honor of the 60th birthday of Professor Kumar Murty. The meetings were focused on several aspects of number theory:

• The theory of automorphic forms and their associated L-functions
• Arithmetic geometry, with special emphasis on algebraic cycles, Shimura varieties, and explicit methods in the theory of abelian varieties
• The emerging applications of number theory in information technology

Kumar Murty has been a substantial influence in these topics, and the two conferences were aimed at honoring his many contributions to number theory, arithmetic geometry, and information technology.

Contains research articles in applications in number theory in information technology with emphasis on cryptographic applications of abelian varieties

Features research articles on explicit methods in abelian varieties, whose explicit constructions will be essential for applications in IT

Addresses questions such as twin rime conjectures with an overview of recent developments in Sieve theory

Klappentext

This volume contains proceedings of two conferences held in Toronto (Canada) and Kozhikode (India) in 2016 in honor of the 60th birthday of Professor Kumar Murty. The meetings were focused on several aspects of number theory:

The theory of automorphic forms and their associated L-functions
Arithmetic geometry, with special emphasis on algebraic cycles, Shimura varieties, and explicit methods in the theory of abelian varieties
The emerging applications of number theory in information technology

Kumar Murty has been a substantial influence in these topics, and the two conferences were aimed at honoring his many contributions to number theory, arithmetic geometry, and information technology.

Inhalt
Overview of the work of Kumar Murty (A. Akbary, S. Gun, M. Ram Murty).- On the average value of a function of the residual index (A. Akbary, A. T. Felix).- Applications of the square sieve to a conjecture of Lang and Trotter for a pair of elliptic curves over the rationals (S. Baier, V. M. Patankar).- $R$-group and multiplicity in restriction for unitary principal series of $GSpin$ and $Spin$ (D. Ban, K. Choiy, D. Goldberg).- The $2$-Class Tower of $\mathbb{Q}(\sqrt{-5460})$ (N. Boston, J. Wang).- On the bad reduction of certain $U(2,1)$ Shimura varieties (E. de Shalit, E. Goren).- Density modulo 1 of a sequence associated to a multiplicative function evaluated at polynomial arguments (J.-M. Deshouillers, M. Nasiri-Zare).- Uniqueness Results for a class of $L$-functions (A. Dixit).- Quadratic periods of meromorphic forms on punctured Riemann surfaces (P. Eskandari).- On the local coefficients matrix for coverings of $\SL_2$ (F. Gao, F. Shahidi, D. Szpruch).- Eisenstein series of weight one, $q$-averages of $0$-logarithm and periods of elliptic curves (D. R. Grayson, D. Ramakrishnan).- On zeros of certain cusp Forms of integral weight for full modular group (M. Manickam, Sandeep E. M.).- A note on Burgess bound (R. Munshi).- A smooth Selberg sieve and applications (M. Ram Murty, A. Vatwani).- Explicit arithmetic on abelian varieties (V. Kumar Murty, P. Sastry).- Derived categories of moduli spaces of vector bundles on curves II (M. S. Narasimhan).- Representations of an integer by some quaternary and octonary quadratic forms (B. Ramakrishnan, B. Sahu, A. K. Singh).- A topological realization of the congruence subgroup kernel (J. Scherk).- Fine Selmer groups and isogeny invariance (R. Sujatha, M. Witte).- Distribution of a subset of non-residues modulo $p$ (by R. Thangadurai, V. Kumar).- On solving a generalized Chinese remainder theorem in the presence of remainder errors (G. Xu).- Endomorphism algebras of abelian varieties with special reference to superelliptic Jacobians Y. G. Zarhin).

## Produktinformationen

 Titel: Geometry, Algebra, Number Theory, and Their Information Technology Applications Untertitel: Toronto, Canada, June, 2016, and Kozhikode, India, August, 2016 Editor: EAN: 9783030073466 ISBN: 3030073467 Format: Kartonierter Einband Herausgeber: Springer International Publishing Genre: Mathematik Anzahl Seiten: 536 Gewicht: 803g Größe: H235mm x B155mm x T28mm Jahr: 2019 Auflage: Softcover reprint of the original 1st ed. 2018

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