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

Chapter 1 Overview of the Work of Kumar Murty

Chapter 2 On the Average Value of a Function of the Residual Index

Chapter 3 Applications of the Square Sieve to a Conjecture of Lang and Trotter for a Pair of Elliptic Curves Over the Rationals

Chapter 4 R -Group and Multiplicity in Restriction for Unitary Principal Series of GSpin and  Spin

Chapter 5 The 2-Class Tower of $$\mathbb {Q}(\sqrt{-5460})$$ Q ( - 5460 )

Chapter 6 On the Bad Reduction of Certain U (2, 1) Shimura Varieties

Chapter 7 Density Modulo 1 of a Sequence Associated with a Multiplicative Function Evaluated at Polynomial Arguments

Chapter 8 Uniqueness Results for a Class of L -Functions

Chapter 9 Quadratic Periods of Meromorphic Forms on Punctured Riemann Surfaces

Chapter 10 On the Local Coefficients Matrix for Coverings of $$\mathrm{SL}_2$$ SL 2

Chapter 11 Eisenstein Series of Weight One, q -Averages of the 0-Logarithm and Periods of Elliptic Curves

Chapter 12 On Zeros of Certain Cusp Forms of Integral Weight for Full Modular Group

Chapter 13 A Note on Burgess Bound

Chapter 14 A Smooth Selberg Sieve and Applications

Chapter 15 Explicit Arithmetic on Abelian Varieties

Chapter 16 Derived Categories of Moduli Spaces of Vector Bundles on Curves II

Chapter 17 Representations of an Integer by Some Quaternary and Octonary Quadratic Forms

Chapter 18 A Topological Realization of the Congruence Subgroup Kernel

Chapter 19 Fine Selmer Groups and Isogeny Invariance

Chapter 20 Distribution of a Subset of Non-residues Modulo p

Chapter 21 On Solving a Generalized Chinese Remainder Theorem in the Presence of Remainder Errors

Chapter 22 Endomorphism Algebras of Abelian Varieties with Special Reference to Superelliptic Jacobians