**Syllabus:**

Name of the Speaker with Affiliation |
Lectures |
Detailed Syllabus |

A. Mukhopadyaya,IMSc, Chennai (AM) |
4 (6 hours) |
Dirichlet Character and Dirichlet Prime NumberTheorem |

S. A. Katre, University of Poona, Pune (SA) |
4 (6hours) | Distribution of Prime Numbers which includes infinitude of prime numbers, Chebychev estimate, Betrands postulate, elementary prime number theorem. |

S. D. Adhikari,HRI, Allahabad (SDA) |
4 (6 hours) | Congruences includes basic linear congruences, Chinese Reminder Theorem, quadratic congruences, quadratic reciprocity law, finding square-root modulo prime and Lagrange Theorem for Polynomial congruences |

M. Manickam, KSOM, Calicut (MM) |
4 (6 hours) | Distribution of Prime Numbers which includes infinitude of prime numbers, Chebychev estimate, Betrands postulate, elementary prime number theorem.Congruences includes basic linear congruences, Chinese Reminder Theorem, quadratic congruences, quadratic reciprocity law, finding square-root modulo prime and Lagrange Theorem for Polynomial congruences |

R. Thangadurai,HRI,Allahabad (RT) |
4 (6 hours) | Induction (weak, strong) equivalent to the well - ordering principle,Decimal expansion of real numbers in base b, Continued fractions of real numbers. |

B. Ramakrishnan,HRI, Allahabad (BR) |
4 (6 hours) | Arithmetical functions, summatory functions, partial summation formula, its application to summatory functions and estimates. |

*SDA and SA sharing topics with MM

**References:**

1.Introduction to Analytical Number Theory by Tom M Apostol

**Time-Table** (with initials of speakers and course associates for entire days of the programme ):

Day |
Date |
Lecture 1(9.30–11.00) |
Tea(11.00–11.30) |
Lecturer 2(11.30–1.00) |
Lunch(1.00–2.30) |
Tutorial 1(2.30–3.30) |
Tea(3.30-4.00) |
Tutorial 2(4.00-5.00) |
Snacks5.00-5.30 |

Mon | 05-10-2015 | RT | BR | Tut | Tut | ||||

Tue | 06-10-2015 | RT | BR | Tut | Tut | ||||

Wed | 07-10-2015 | RT | BR | Tut | Tut | ||||

Thu | 08-10-2015 | RT | BR | Tut | Tut | ||||

Fri | 09-10-2015 | SA | SDA | Tut | Tut | ||||

Sat | 10-10-2015 | SA | SDA | Tut | Tut | ||||

Sunday | |||||||||

Mon | 12-10-2015 | SA | SDA | Tut | Tut | ||||

Tue | 13-10-2015 | SA | SDA | Tut | Tut | ||||

Wed | 14-10-2015 | AM | MM | Tut | Tut | ||||

Thu | 15-10-2015 | AM | MM | Tut | Tut | ||||

Fri | 16-10-2015 | AM | MM | Tut | Tut | ||||

Sat | 17-10-2015 | AM | MM | Tut | Tut |