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The Fine-Structure Hierarchy of Prime Biases and the Universal Dominance of
Shin-ya Koyama
We investigate the deterministic hierarchy of prime distribution biases in arithmetic progressions modulo using a regularized spectral approach. Classical studies on Chebyshev'…
Chebyshev's bias for modular forms
Shin-ya Koyama, Arshay Sheth
We study Chebyshev's bias for the signs of Fourier coefficients of cuspidal newforms on . Our main result shows that the bias towards either sign is completely determined b…
Chebyshev's Bias for Ramanujan's -function via the Deep Riemann Hypothesis
Shin-ya Koyama, Nobushige Kurokawa
The authors assume the Deep Riemann Hypothesis to prove that a weighted sum of Ramanujan's -function has a bias to being positive. This phenomenon is an analogue of Chebyshev's…
Variations of Ramanujan's Euler Products
Shin-ya Koyama, Nobushige Kurokawa
We study the meromorphy of various Euler products of degree two attached to cusp forms including Ramanujan's -function.
Rigidity of Euler Products
Shin-ya Koyama, Nobushige Kurokawa
We report a simple rigidity theorem for certain Euler products.
Functional equations for Selberg zeta functions with Tate motives
Shin-ya Koyama, Nobushige Kurokawa
For a compact Riemann surface of genus , we study the functional equations of the Selberg zeta functions attached with the Tate motives . We prove that certain funct…