Spring 2027

Analytic Number Theory

Introduction to the Riemann zeta function and Dirichlet L-functions in Analytic Number Theory, applied to prime distribution and quadratic field arithmetic.

no offering record for this termCredits unavailable
Recorded instructors · Spring 2027 No instructors listed

Summary

1 / 4

Recent recorded grades — Fall 2019: 3.93 GPA, 100.0% A/AB (n=14 letter grades); Fall 2021: 4.00 GPA, 100.0% A/AB (n=16 letter grades); Fall 2023: 3.93 GPA, 100.0% A/AB (n=15 letter grades).

What you’ll be able to do

  • Examine a range of mathematical proofs and identify underlyingprinciples and techniques.

  • Write clear and well-reasoned mathematical arguments.

  • Explain the methods used to establish the analytic continuation andfunctional equation of the Riemann zeta function and Dirichlet L-functions.

  • Apply tools from complex analysis to analyze the distribution ofzeros of L-functions.

  • Apply the above results on the zeros of L-functions to analyze thedistribution of prime numbers.

Source: UW Guide

Grade history

↗
average GPA
letter grades
A
AB
B
BC
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Prerequisites

Course map

Graduate/professional standing or declared in Mathematics VISP (graduate or dissertator)

    • Graduate/professional standing
    • declared in Mathematics VISP (graduate or dissertator)
    take one
MATH 749

This is a best-effort interpretation; check the catalog requirements above.

Prerequisite text tree
  • Any of
    • Graduate/professional standing
    • declared in Mathematics VISP (graduate or dissertator)

Professors

Spring 2027

No instructors recorded for this selection.

Historical instructors & teaching patterns

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Calendar & sections

Spring 2027

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Student experience

the class

Recent recorded grades — Fall 2019: 3.93 GPA, 100.0% A/AB (n=14 letter grades); Fall 2021: 4.00 GPA, 100.0% A/AB (n=16 letter grades); Fall 2023: 3.93 GPA, 100.0% A/AB (n=15 letter grades).

difficulty & workload

No workload feedback recorded.

Topics

  • Riemann zeta function and Dirichlet L-functions
  • Distribution of prime numbers
  • Arithmetic of quadratic fields

Skills

  • Establish analytic continuation and functional equations for Riemann zeta and Dirichlet L-functions
  • Analyze the distribution of zeros of L-functions using complex analysis
  • Analyze the distribution of prime numbers using results on L-function zeros

Grades

Latest available · Fall 2023— not enough history to project Spring 2027.

average GPA
A / AB grades
letter grades
Instructor

Grade distribution · % of letter grades

A
AB
B
BC
C
D
F

Grades over time

Through Fall 2023

More grade details Grade mix, volume & source data

Not enough comparable courses for Spring 2027 in UW–Madison.

Sources & history

UW–Madison

Catalog & offerings

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Dataset & model

Recorded 2026-10-14

View the dataset on Hugging Face
Model outputs & technical records
Qwen/Qwen3.8-27B
LLM outputs across runs
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Full model traces

Recorded model configuration, reasoning, and tool conversations.

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Model & dataset provenance 
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  "model": "Qwen/Qwen3.8-27B",
  "model_revision": "1d4bf0f2ff6012fd82039f2fa52739d0dd7c60c0",
  "task_version": "17",
  "output_id": "66911f4ee84c6ee8922f3c69e978a3aedf0e8738a0cca0b9b21cdae44b977f9b",
  "requirements_status": "needs_review",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}