权重≤p+1的非普通模形式的带符号p进L函数的典范构造
A canonical construction of signed $p$-adic $L$-functions for non-ordinary modular forms of weight $\leq p+1$
AI总结：
本文针对权重≤p+1的p-非普通模形式，通过无需p进霍奇理论的显式对数型矩阵分解无界p进L函数，构造出一对有界p进L函数，还计算了相关Iwasawa不变量的渐近公式并推广了已有结果。
AI中文摘要：
取奇素数p，设f为权重2≤k≤p+1的p-非普通尖点特征新形式。我们通过依据显式对数型矩阵分解无界p进L函数来构造与f相关的一对有界p进L函数，该矩阵的定义无需p进霍奇理论。利用此分解，我们计算权重≤p+1的非普通形式对应的Mazur-Tate元的Iwasawa不变量的渐近公式。作为推论，我们得到权重2与p+1的p-非普通及p-同余尖点形式的带符号Iwasawa不变量之间的关系，推广了a_p=0情形的已有结果。
英文摘要：
Fix an odd prime $p$ and let $f$ be a $p$-non-ordinary cuspidal eigen-newform of weight $2\leq k\leq p+1$. We construct a pair of bounded $p$-adic $L$-functions associated to $f$ by decomposing the unbounded $p$-adic $L$-functions in terms of an explicit logarithm-type matrix whose definition does not require $p$-adic Hodge theory. Using this decomposition, we compute asymptotic formulas for the Iwasawa invariants of Mazur--Tate elements attached to non-ordinary forms of weight $\leq p+1$. As a corollary, we obtain a relation between the signed Iwasawa invariants of $p$-non-ordinary and $p$-congruent cuspforms of weights 2 and $p+1$, generalizing previous results in the $a_p=0$ case.
