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A reciprocity relation for the twisted second moment of the Riemman Zeta function

Rizwanur Khan

Abstract

We prove a reciprocity relation for the twisted second moment of the Riemann Zeta function. This provides an analogue to a formula of Conrey for Dirichlet L-functions

A reciprocity relation for the twisted second moment of the Riemman Zeta function

Abstract

We prove a reciprocity relation for the twisted second moment of the Riemann Zeta function. This provides an analogue to a formula of Conrey for Dirichlet L-functions
Paper Structure (11 sections, 2 theorems, 40 equations)

This paper contains 11 sections, 2 theorems, 40 equations.

Table of Contents

  1. Introduction
  2. Sketch
  3. Proof of Theorem \ref{['main']}
  4. Set up
  5. Functional equation
  6. Opening an oscillatory factor
  7. Averaging over the family (evaluating the integral on the critical line)
  8. An approximation
  9. Averaging over the family (evaluating the character sum and integral on the critical line)
  10. Opening the oscillatory factor (Gauss sum)
  11. Applying the functional equation

Key Result

Theorem 1

Let $p$ and $q$ be distinct odd primes. Let $T>1$. We have

Theorems & Definitions (2)

  • Theorem 1
  • Corollary 2