Current Trends in Number Theory

Description

Front Matter ....Pages i-ix On the Average of the Sum-of-odd-divisors Function (S. D. Adhikari, G. Coppola)....Pages 1-15 Rogers-Ramanujan Identities (A. K. Agarwal)....Pages 17-25 On the Problem of Explicit Evaluation of the Number of Solutions of the Equation a1x12 + ⋯ + anxn2 = bx1 ⋯ xn in a Finite Field (Ioulia Baoulina)....Pages 27-37 An Introduction to Congruences Between Modular Forms (Eknath Ghate)....Pages 39-58 The Cyclotomic Problem (S. A. Katre)....Pages 59-72 The Local Root Number of Elliptic Curves (Shin-Ichi Kobayashi)....Pages 73-83 On Skew-holomorphic Jacobi Forms (M. Manickam)....Pages 85-90 The View-obstruction Problem (Anirban Mukhopadhyay)....Pages 91-100 The Addition Law on Hyperelliptic Jacobians (V. Kumar Murty)....Pages 101-110 Sieving Using Dirichlet Series (M. Ram Murty)....Pages 111-124 Higher Circular ℓ-units of Anderson and Ihara (D. S. Nagaraj)....Pages 125-128 On Automorphism Groups of Algebraic Curves (Shōichi Nakajima)....Pages 129-134 Special Integral Bases with Restricted Coefficients for Extensions of Dedekind Domains (V. C. Nanda)....Pages 135-140 Zeta Functions for Curves Defined over Finite Fields (Anuradha Narasimhan)....Pages 141-146 Algebraic Elements in Group Rings (I. B. S. Passi)....Pages 147-158 Reflection Representation and Theta Correspondence (Nilabh Sanat)....Pages 159-164 Some Aspects of the Central Critical Value of Automorphic L-functions (J. Sengupta)....Pages 165-174 Integral Points on the Circle X2 + Y2 = c (Parvati Shastri)....Pages 175-184 An Equation of Goormaghtigh and Diophantine Approximations (T. N. Shorey)....Pages 185-197 Base Change, Distinguishedness and a Theorem of Saito (Rajat Tandon)....Pages 199-213 Elliptic curves in function field arithmetic (Dinesh S. Thakur)....Pages 215-238 On Certain Zero-sum Problems in Finite Abelian Groups (R. Thangadurai)....Pages 239-254 Modular Forms and Functional Equations (T. C. Vasudevan)....Pages 255-264 Lefschetz Properties of Subvarieties of Shimura Varieties (T. N. Venkataramana)....Pages 265-270