On sums involving products and quotients of L-functions over function fields

2013/10/31 by Jeffrey Lin Thunder, Thunder, Jeffrey Lin
Computer Science · Mathematics · #11M41 #11S40 #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M41 #msc:11S40

paper · pdf · doi:10.48550/arxiv.1310.8572

59 pages

arxiv created 2013/10/31 · openalex publication_date 2013/10/31 · arxiv updated 2013/11/01 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We estimate the sum of products or quotients of L-functions, where the sum is taken over all quadratic extensions of given genus over a fixed global function field. Our estimate for the sum of the quotient of two L-functions is analogous to a result of Schmidt where he estimates the sum of the quotient of two L-series, where the sum is over quadratic extensions of \bq with absolute value of the discriminant less than a given bound.

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• Sums of L-functions over the rational function field
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• Average values of L-functions in even characteristic
• A sum-product theorem in function fields