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<p>The aim of this paper is to determine all algebraic relations among various special gamma values over function fields, and prove a Chowla–Selberg-type formula for quasi-periods of CM abelian <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi>t</mi> </math></EquationSource> <EquationSource Format="TEX">$t$</EquationSource> </InlineEquation>-modules. Our results are based on the intrinsic relations between gamma values in question and periods of CM dual <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mi>t</mi> </math></EquationSource> <EquationSource Format="TEX">$t$</EquationSource> </InlineEquation>-motives, which are interpreted in terms of their “distributions”. This also enables us to derive an analogue of the Deligne–Gross period conjecture for CM Hodge–Pink structures.</p>

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Algebraic relations among special gamma values and the Chowla–Selberg phenomenon over function fields

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  • 发表日期：

    2026年1月23日

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  • Fu-Tsun Wei

摘要

The aim of this paper is to determine all algebraic relations among various special gamma values over function fields, and prove a Chowla–Selberg-type formula for quasi-periods of CM abelian t $t$ -modules. Our results are based on the intrinsic relations between gamma values in question and periods of CM dual t $t$ -motives, which are interpreted in terms of their “distributions”. This also enables us to derive an analogue of the Deligne–Gross period conjecture for CM Hodge–Pink structures.